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Modular Cohomology Rings of some Finite Groups
The data presented here were computed using version 2.0 of
our Sage
cohomology package.
| Group | Mod 2 | Mod 3 | Mod 5 | Mod 7 | Mod 11 | Mod 13 | Mod 17 | Mod 19 | 23 |
| Sporadic Groups (without Mathieu groups) |
| Co3 |
H*(Co3;GF(2)) |
|
H*(Co3;GF(5)) |
| HS |
H*(HS;GF(2)) |
H*(HS;GF(3)) |
H*(HS;GF(5)) |
| J1 |
H*(J1;GF(2)) |
H*(J1;GF(3)) |
H*(J1;GF(5)) |
H*(J1;GF(7)) |
H*(J1;GF(11)) |
| |
H*(J1;GF(19)) |
| J2 |
H*(J2;GF(2)) |
H*(J2;GF(3)) |
H*(J2;GF(5)) |
H*(J2;GF(7)) |
| J3 |
H*(J3;GF(2)) |
H*(J3;GF(3)) |
H*(J3;GF(5)) |
| | |
H*(J3;GF(17)) |
H*(J3;GF(19)) |
| McL |
H*(McL;GF(2)) |
|
H*(McL;GF(5)) |
H*(McL;GF(7)) |
H*(McL;GF(11)) |
| Mathieu groups |
| M9 |
H*(M9;GF(2)) |
H*(M9;GF(3)) |
| M10 |
H*(M10;GF(2)) |
H*(M10;GF(3)) |
H*(M10;GF(5)) |
| M11 |
H*(M11;GF(2)) |
H*(M11;GF(3)) |
H*(M11;GF(5)) |
|
H*(M11;GF(11)) |
| M12 |
H*(M12;GF(2)) |
H*(M12;GF(3)) |
H*(M12;GF(5)) |
|
H*(M12;GF(11)) |
| M21 |
H*(M21;GF(2)) |
H*(M21;GF(3)) |
H*(M21;GF(5)) |
H*(M21;GF(7)) |
| M22 |
H*(M22;GF(2)) |
H*(M22;GF(3)) |
H*(M22;GF(5)) |
H*(M22;GF(7)) |
H*(M22;GF(11)) |
| M23 |
H*(M23;GF(2)) |
H*(M23;GF(3)) |
H*(M23;GF(5)) |
H*(M23;GF(7)) |
H*(M23;GF(11)) |
| | |
H*(M23;GF(23)) |
| Alternating Groups |
| A4 |
H*(A4;GF(2)) |
H*(A4;GF(3)) |
| A5 |
H*(A5;GF(2)) |
H*(A5;GF(3)) |
H*(A5;GF(5)) |
| A6 |
H*(A6;GF(2)) |
H*(A6;GF(3)) |
H*(A6;GF(5)) |
| A7 |
H*(A7;GF(2)) |
H*(A7;GF(3)) |
H*(A7;GF(5)) |
H*(A7;GF(7)) |
| A8 |
H*(A8;GF(2)) |
H*(A8;GF(3)) |
H*(A8;GF(5)) |
H*(A8;GF(7)) |
| A9 |
H*(A9;GF(2)) |
H*(A9;GF(3)) |
H*(A9;GF(5)) |
H*(A9;GF(7)) |
| A10 |
H*(A10;GF(2)) |
H*(A10;GF(3)) |
H*(A10;GF(5)) |
H*(A10;GF(7)) |
| A11 |
H*(A11;GF(2)) |
H*(A11;GF(3)) |
H*(A11;GF(5)) |
H*(A11;GF(7)) |
H*(A11;GF(11)) |
| Symmetric Groups |
| Sym4 |
H*(Sym4;GF(2)) |
H*(Sym4;GF(3)) |
| Sym5 |
H*(Sym5;GF(2)) |
H*(Sym5;GF(3)) |
H*(Sym5;GF(5)) |
| Sym6 |
H*(Sym6;GF(2)) |
H*(Sym6;GF(3)) |
H*(Sym6;GF(5)) |
| Sym7 |
H*(Sym7;GF(2)) |
H*(Sym7;GF(3)) |
H*(Sym7;GF(5)) |
H*(Sym7;GF(7)) |
| Sym8 |
H*(Sym8;GF(2)) |
H*(Sym8;GF(3)) |
H*(Sym8;GF(5)) |
H*(Sym8;GF(7)) |
| Sym9 |
H*(Sym9;GF(2)) |
H*(Sym9;GF(3)) |
H*(Sym9;GF(5)) |
H*(Sym9;GF(7)) |
| Sym10 |
H*(Sym10;GF(2)) |
H*(Sym10;GF(3)) |
H*(Sym10;GF(5)) |
H*(Sym10;GF(7)) |
| Exceptional Groups of Lie Type |
| G2(3) |
H*(G2(3);GF(2)) |
|
|
H*(G2(3);GF(7)) |
|
H*(G2(3);GF(13)) |
| G2(5) |
H*(G2(5);GF(2)) |
H*(G2(5);GF(3)) |
| Sz(8) |
H*(Sz(8);GF(2)) |
|
H*(Sz(8);GF(5)) |
H*(Sz(8);GF(7)) |
|
H*(Sz(8);GF(13)) |
| Linear Groups |
| Special Linear Groups |
| SL(3,4) |
H*(SL(3,4);GF(2)) |
H*(SL(3,4);GF(3)) |
H*(SL(3,4);GF(5)) |
H*(SL(3,4);GF(7)) |
| SL(4,3) |
H*(SL(4,3);GF(2)) |
| Symplectic Groups |
| Sp(4,3) |
H*(Sp(4,3);GF(2)) |
H*(Sp(4,3);GF(3)) |
H*(Sp(4,3);GF(5)) |
| Sp(4,5) |
H*(Sp(4,5);GF(2)) |
|
|
|
|
H*(Sp(4,5);GF(13)) |
| Sp(4,8) |
|
H*(Sp(4,8);GF(3)) |
| Sp(6,4) |
|
H*(Sp(6,4);GF(3)) |
H*(Sp(6,4);GF(5)) |
| Sp(8,2) |
|
H*(Sp(8,2);GF(3)) |
| Unitary Groups |
| U3(3) |
H*(U3(3);GF(2)) |
H*(U3(3);GF(3)) |
|
H*(U3(3);GF(7)) |
| U3(4) |
H*(U3(4);GF(2)) |
H*(U3(4);GF(3)) |
H*(U3(4);GF(5)) |
|
|
H*(U3(4);GF(13)) |
| More Groups |
| J3.2 |
H*(J3.2;GF(2)) |
|
H*(J3.2;GF(5)) |
| | |
H*(J3.2;GF(17)) |
H*(J3.2;GF(19)) |
| L2(8).3 |
H*(L2(8).3;GF(2)) |
H*(L2(8).3;GF(3)) |
|
H*(L2(8).3;GF(7)) |
| L3(3).2 |
H*(L3(3).2;GF(2)) |
H*(L3(3).2;GF(3)) |
| | |
H*(L3(3).2;GF(13)) |
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