Finite Group Databasebeta

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C₂²×#7967933 #72336995

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

Aliases

Subgroups

At least 10602 conjugacy classes of subgroups; only the 445696 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

404 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((17,18,21,22)(19,20,23,24), (6,8)(18,22)(20,24), (9,10)(11,14)(12,13)(15,16)(17,19)(18,20)(21,23)(22,24), (6,8)(10,13)(14,15)(17,19)(18,20)(21,23)(22,24), (3,4), (6,8)(9,11)(10,14)(12,16)(13,15)(17,19)(18,20)(21,23)(22,24), (1,2)(3,4), (5,6)(7,8)(9,10)(11,15)(12,13)(14,16)(17,20)(18,23)(19,22)(21,24));