Finite Group Databasebeta

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C₂²×#7708349 #72296076

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

Aliases

Subgroups

At least 6690 conjugacy classes of subgroups; only the 446600 normal subgroups are shown.

Full subgroup data →

Presentation

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

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