Finite Group Databasebeta

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C₂²×#44871 #72299729

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

Aliases

Subgroups

106785 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((6,8)(17,18,21,24)(19,22,23,20), (5,6)(7,8)(11,15)(14,16), (10,13)(14,16)(17,19)(18,22)(20,24)(21,23), (9,10)(11,16)(12,13)(14,15)(17,19)(18,22)(20,24)(21,23), (9,11)(10,14)(12,15)(13,16)(17,20,21,22)(18,23,24,19), (3,4), (1,2)(3,4));