Finite Group Databasebeta

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C₂²×#12697 #72306500

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

Aliases

Subgroups

40869 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

136 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), (6,8)(9,10)(11,18,19,14)(12,17,21,15)(13,16)(20,22)(23,24), (5,6)(7,8)(9,11)(10,14)(12,20)(13,19)(15,22)(16,18)(17,23)(21,24), (3,4), (10,15)(12,21)(14,22)(16,17)(18,23)(20,24));