Finite Group Databasebeta

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C₂³×#36212 #72324536

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

Aliases

Subgroups

5895240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 22 points:

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

Conjugacy classes & character table

560 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((11,12)(13,14)(15,16,18,19)(17,20,22,21), (16,19)(20,21), (3,4), (5,6), (11,12)(13,14)(15,17,18,22)(16,20,19,21), (1,2)(3,4)(5,6), (8,10)(12,14)(15,17)(16,21)(18,22)(19,20), (7,8)(9,10)(11,12)(13,14)(15,16)(17,20)(18,19)(21,22));