Finite Group Databasebeta

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C₂³×#2656 #72289385

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

Aliases

Subgroups

213317 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((8,10)(12,13)(15,16,18,20)(17,19,22,21), (3,4), (8,10)(11,12)(13,14)(15,16,18,20)(17,21,22,19), (8,10)(12,13)(15,16)(17,19)(18,20)(21,22), (7,8,9,10)(11,13,14,12)(15,17)(16,19)(18,22)(20,21), (5,6), (1,2)(3,4)(5,6));