Finite Group Databasebeta

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C₂²×#11129 #72316925

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

Aliases

Subgroups

29141 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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