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C₂²×#39460 #72324722

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

Aliases

Subgroups

111609 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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)(9,10,13,16)(11,12,15,14)(17,18,21,23)(19,22,24,20), (5,6)(7,8)(9,11,13,15)(10,14,16,12)(17,19,21,24)(18,22,23,20), (18,23)(19,24), (3,4), (1,2)(3,4), (6,8)(9,11)(10,14)(12,16)(13,15)(17,20)(18,19)(21,22)(23,24), (5,6)(7,8)(9,12,13,14)(10,15,16,11)(17,19)(18,22)(20,23)(21,24));