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C₂²×#34493 #72301000

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

Aliases

Subgroups

116209 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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