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C₂²×#7722013 #72325847

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

Aliases

Subgroups

1481224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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