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C₂²×#35031 #72324588

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

Aliases

Subgroups

114965 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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