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C₂²×#517979 #72320891

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

Aliases

Subgroups

788912 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

512 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((3,4), (5,6,8,7)(13,14,16,15)(17,18)(19,22)(20,21)(23,24), (9,10,12,11)(13,14,16,15)(18,21)(19,23), (6,7)(14,15), (1,2)(3,4), (17,18)(19,24)(20,21)(22,23), (5,7,8,6)(9,11,12,10)(13,15,16,14)(17,19,20,23)(18,22,21,24));