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C₂²×C₈×M₃₂ #72226977

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

Aliases

Subgroups

5229 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

(1,2);(13,14,15,19,16,20,21,26,17,18,22,24,23,25,27,28);(5,6,7,9,8,10,11,12);(3,4);(14,18)(19,24)(20,25)(26,28)

Conjugacy classes & character table

640 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((1,2), (13,14,15,19,16,20,21,26,17,18,22,24,23,25,27,28), (5,6,7,9,8,10,11,12), (3,4), (14,18)(19,24)(20,25)(26,28));