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C₂²×#34205 #72293717

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

Aliases

Subgroups

146877 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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