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C₂²×#45140 #72292910

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

Aliases

Subgroups

111813 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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