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C₂²×#1409001 #72320871

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

808820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

(3,4);(9,10,12,11)(13,14,16,15)(17,18)(19,20)(21,23)(22,24);(5,6)(7,8)(13,14,16,15)(17,19,21,24)(18,22,23,20);(6,8)(10,11)(14,15)(17,20,21,22)(18,19,23,24);(1,2)(3,4);(6,8)(9,11,12,10)(13,15,16,14)(17,20)(18,19)(21,22)(23,24);(5,6)(7,8)(17,18)(19,22)(20,24)(21,23)

Conjugacy classes & character table

344 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((3,4), (9,10,12,11)(13,14,16,15)(17,18)(19,20)(21,23)(22,24), (5,6)(7,8)(13,14,16,15)(17,19,21,24)(18,22,23,20), (6,8)(10,11)(14,15)(17,20,21,22)(18,19,23,24), (1,2)(3,4), (6,8)(9,11,12,10)(13,15,16,14)(17,20)(18,19)(21,22)(23,24), (5,6)(7,8)(17,18)(19,22)(20,24)(21,23));