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C₂²×#59030 #72300993

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

Aliases

Subgroups

115457 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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