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C₂²×D₄×#546 #72324181

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

Aliases

Subgroups

At least 7095 conjugacy classes of subgroups; only the 477184 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

500 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), (6,8)(10,11)(13,14)(15,16)(17,18)(19,20), (6,8)(9,11,12,10)(14,18)(16,20), (3,4), (6,8)(13,15)(14,16)(17,19)(18,20), (1,2)(3,4), (5,6,7,8)(13,16)(14,19)(15,18)(17,20));