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C₂²×#7718113 #72292913

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

Aliases

Subgroups

1564624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

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

Conjugacy classes & character table

392 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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