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C₂²×#35010 #72325837

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

Aliases

Subgroups

114125 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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