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C₂²×#7677118 #72293063

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

Aliases

Subgroups

2092800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 20 points:

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

Conjugacy classes & character table

440 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((6,7)(15,20)(16,19), (3,4), (5,6,8,7)(10,12)(15,20)(16,19), (13,14)(15,19)(16,20)(17,18), (9,10)(11,12)(14,18)(15,20), (1,2)(3,4), (13,15,17,20)(14,19,18,16), (5,7,8,6)(13,16,17,19)(14,20,18,15));