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C₂²×#34204 #72320607

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

Aliases

Subgroups

145829 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

352 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((3,4), (13,14,17,16)(15,18,20,19), (5,6,8,7)(9,10,11,12)(13,14)(15,19)(16,17)(18,20), (9,10)(11,12)(14,16)(18,19), (1,2)(3,4), (13,15)(14,18)(16,19)(17,20), (5,7,8,6)(13,16,17,14)(15,18,20,19));