Finite Group Databasebeta

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C₂²×#7687902 #72301246

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

Aliases

Subgroups

1089836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

452 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)(12,13)(14,16)(17,18)(19,23)(20,24)(21,22), (5,6)(7,8)(9,10)(11,14)(12,13)(15,16), (9,10)(11,15)(12,13)(14,16)(17,19,22,24)(18,20,21,23), (10,13)(11,16)(18,21)(20,23), (9,10)(11,14)(12,13)(15,16)(17,20)(18,19)(21,24)(22,23), (9,11,12,16)(10,14,13,15)(17,21,22,18)(19,20,24,23), (3,4), (1,2)(3,4));