Finite Group Databasebeta

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C₂²×#7733150 #72301009

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

Aliases

Subgroups

At least 6165 conjugacy classes of subgroups; only the 445992 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

416 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)(9,10)(11,15)(12,14)(13,16)(17,18)(19,22)(20,21)(23,24), (5,6)(7,8)(11,16)(13,15)(19,24)(22,23), (17,19)(18,22)(20,23)(21,24), (9,10,12,14)(11,15,16,13)(17,20,21,18)(19,23,24,22), (9,10)(11,13)(12,14)(15,16), (9,11)(10,13)(12,16)(14,15)(17,19)(18,23)(20,22)(21,24), (3,4), (1,2)(3,4));