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C₂²×#35076 #72291831

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

Aliases

Subgroups

135469 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)(19,21)(20,23)(22,24);(17,19,22,23)(18,21,24,20);(9,11)(10,13)(12,16)(14,15)(17,20,22,21)(18,23,24,19);(5,6,7,8)(9,11)(10,14)(12,16)(13,15)(17,21,22,20)(18,23,24,19);(9,10)(11,13)(12,15)(14,16)(17,18)(19,21)(20,23)(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)(11,14)(12,15)(13,16)(17,18)(19,21)(20,23)(22,24), (17,19,22,23)(18,21,24,20), (9,11)(10,13)(12,16)(14,15)(17,20,22,21)(18,23,24,19), (5,6,7,8)(9,11)(10,14)(12,16)(13,15)(17,21,22,20)(18,23,24,19), (9,10)(11,13)(12,15)(14,16)(17,18)(19,21)(20,23)(22,24), (3,4), (1,2)(3,4));