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C₂³×#35527 #72301714

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

Aliases

Subgroups

6109288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

512 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((3,4), (5,6), (1,2)(3,4)(5,6), (7,8,9,10)(11,12,13,14)(15,16,18,20)(17,19,22,21), (7,8)(9,10)(11,12)(13,14)(15,17,18,22)(16,19,20,21), (11,12)(13,14)(16,20)(19,21), (8,10)(11,12,13,14)(15,17)(16,21)(18,22)(19,20), (7,8)(9,10)(11,12)(13,14)(15,16)(17,19)(18,20)(21,22));