Finite Group Databasebeta

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C₂²×#7716499 #72336141

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

Aliases

Subgroups

At least 6834 conjugacy classes of subgroups; only the 445480 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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