Finite Group Databasebeta

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C₂²×#36123 #72278458

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

Aliases

Subgroups

149793 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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