Finite Group Databasebeta

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C₂²×#36213 #72315142

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

Aliases

Subgroups

312353 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

280 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((14,18)(19,20), (13,14)(15,19)(16,20)(17,18), (3,4)(6,8)(9,10,12,11)(13,15,17,16)(14,19,18,20), (1,2)(3,4), (10,11), (6,8)(9,11,12,10)(13,16,17,15)(14,20,18,19), (5,6,7,8)(9,10,12,11));