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C₂²×#10989 #72314743

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

Aliases

Subgroups

49925 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

184 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)(10,15,17,19)(13,21)(16,22,24,23)(18,20), (5,6)(7,8)(10,16)(11,12)(15,22)(17,24)(18,20)(19,23), (5,6)(7,8)(9,10)(11,15)(12,19)(13,16)(14,17)(18,23)(20,22)(21,24), (1,2), (3,4)(5,7)(6,8)(9,11,14,12)(10,15,17,19)(13,18,21,20)(16,23,24,22));