Finite Group Databasebeta

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C₂²×#7779984 #72301232

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

Aliases

Subgroups

1150456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 24 points:

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

Conjugacy classes & character table

392 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)(10,14)(11,16)(17,18)(19,24)(20,23)(21,22), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(19,23)(20,24), (9,11,13,16)(10,15,14,12)(17,19,21,23)(18,20,22,24), (11,16)(12,15)(18,22)(20,24), (9,12)(10,11)(13,15)(14,16)(17,18)(19,20)(21,22)(23,24), (9,11)(10,12)(13,16)(14,15)(17,20)(18,23)(19,22)(21,24), (3,4), (1,2)(3,4));