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C₂²×#36260 #72299853

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

Aliases

Subgroups

171245 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 20 points:

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

Conjugacy classes & character table

280 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((9,10,11,12)(13,14,17,18)(15,16,20,19), (14,18)(16,19), (9,10,11,12)(14,18)(16,19), (6,8)(10,12)(13,15)(14,19)(16,18)(17,20), (5,6)(7,8)(9,10)(11,12)(13,16,17,19)(14,15,18,20), (3,4), (1,2)(3,4));