Finite Group Databasebeta

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C₂²×#34248 #72295850

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

Aliases

Subgroups

144989 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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