David J. Green

Cohomology
→Theory
→Implementation

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Singular

Gap

The Cohomology of the Groups of Order 64

In total, there are 267 groups of order 64. With version 2.1 of our package, using Sage 4.5.2, the total computation time, only occupying one core in each case, was

• less than 13 CPU-minutes (about 18:35 minutes walltime) on a 4-core Mac Pro desktop machine running at 2.6 Ghz with 8 GB RAM (Darwin Kernel Version 10.0.0) in 64 bit mode; we are grateful to William Stein for giving us access to this machine.
• about 19 CPU-minutes (about 35:20 minutes walltime) on an Intel Core 2 CPU running at 2.6 Ghz with 2 GB RAM (openSUSE 11.0).
• about 33 CPU-minutes (about 61 minutes walltime) on a Dual Core AMD Opteron(tm) Processor 270 running at 2.0 GHz with 16 GB RAM (openSUSE 10.2).

Groups numbered according to the Small Groups library

Groups with a custom name

Central product E32+ * C_4

Dihedral group of order 64

Direct product D8 x V_8

Direct product Q8 x Q8

Direct product Q8 x V_8

Modular group of order 64

Quaternion group of order 64

Semidihedral group of order 64

Sylow 2-subgroup of L_3(4)

Sylow 2-subgroup of A_8=L_4(2)

Sylow 2-subgroup of Mathieu Group M_12

Sylow 2-subgroup of Suzuki Group Sz(8)

Sylow 2-subgroup of U_3(4)