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C₂²×#12928 #72309873

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

Aliases

Subgroups

8289 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

184 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((1,2)(3,4)(6,8)(10,14,15,20)(11,17)(12,19)(16,23,22,21)(18,24), (1,2)(3,4)(5,6)(7,8)(10,15)(14,20)(16,22)(21,23), (6,8)(9,10,11,14,12,16,17,21,13,15,18,20,19,22,24,23), (1,2), (3,4));