This library gives explicit access to the following groups of order 1024:
The rank 1 group
All rank 2 groups
All rank 3 groups
All rank 4 groups
Rank 5 groups with p-class at least 3
Rank 6 groups with p-class at least 3
Rank 7 groups with p-class at least 3
Rank 8 groups with p-class at least 3
Rank 9 groups with p-class at least 3
The rank 10 group
This library gives partial information on the remaining groups of order 1024:
Rank 5 groups with p-class 2
Rank 6 groups with p-class 2
Rank 7 groups with p-class 2
Rank 8 groups with p-class 2
Rank 9 groups with p-class 2
For the groups that are not explicitly available the following information is available:
Parent Group ID
Parent Group Order
p-class
Rank
Age
The groups are sorted first by their parent group ids and then by the pc codes of the standard presentations for the groups. The data contained in this library was used in the 2021 enumeration of the groups of order 1024 [Bur22]. The available groups were generated using the p-group generation algorithm [O'B90] as implemented in the ANUPQ package [GNOH19]. The information on the remaining groups was calculated using the cohomological methods for enumerating p-groups of p-class 2 as introduced in [EO99].
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