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C₂³×#44870 #72289514

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

Aliases

Subgroups

2385648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

464 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)(17,20)(18,21)(19,22), (11,12)(13,14)(15,17)(16,18)(19,21)(20,22), (7,8)(9,10)(11,12,13,14), (8,9)(11,12)(13,14)(15,17)(16,20)(18,22)(19,21), (7,9,10,8)(15,18,19,20)(16,21,22,17), (3,4), (5,6), (1,2)(3,4)(5,6));