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C₂²×#7645254 #72336357

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

Aliases

Subgroups

1552928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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