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C₂²×#59420 #72300995

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

Aliases

Subgroups

115137 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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