Finite Group Databasebeta

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C₂²×#34210 #72293060

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

Aliases

Subgroups

162469 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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