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C₂²×D₄×#534 #72324162

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

Aliases

Subgroups

2238064 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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