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C₂²×#34477 #72299870

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

Aliases

Subgroups

91929 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((10,13)(11,15)(17,18)(19,22)(20,24)(21,23), (10,13)(14,16)(17,19,21,24)(18,22,23,20), (11,15)(14,16)(17,19)(18,20)(21,24)(22,23), (5,6,7,8)(9,10,12,13)(11,14,15,16), (9,11)(10,14)(12,15)(13,16)(17,20)(18,19)(21,22)(23,24), (3,4), (1,2)(3,4));