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C₂³×#2445 #72325056

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

Aliases

Subgroups

170229 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((7,8)(9,10)(12,14)(16,19)(17,21), (7,8,9,10), (3,4), (5,6), (8,10)(11,12,13,14)(15,16)(17,22)(18,19)(20,21), (1,2)(3,4)(5,6), (7,8)(9,10)(15,17)(16,20)(18,21)(19,22));