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C₂²×#35694 #72296529

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

Aliases

Subgroups

121045 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

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

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