Finite Group Databasebeta

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C₂²×#36154 #72299823

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

Aliases

Subgroups

113353 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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