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C₂²×#35222 #72256555

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

Aliases

Subgroups

491645 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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