Finite Group Databasebeta

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C₂²×#36158 #72296000

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

Aliases

Subgroups

205201 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

280 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((6,8)(9,10,12,15)(11,14,16,13)(17,18,21,22)(19,20,23,24), (5,6,7,8)(9,11,12,16)(10,13,15,14)(17,19,21,23)(18,20,22,24), (9,11)(10,14)(12,16)(13,15)(17,19)(18,20)(21,23)(22,24), (17,20)(18,19)(21,24)(22,23), (5,6)(7,8)(9,10)(11,14)(12,15)(13,16)(17,20)(18,19)(21,24)(22,23), (3,4), (1,2)(3,4));