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C₂²×#35063 #72325823

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

Aliases

Subgroups

116013 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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