Finite Group Databasebeta

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C₂²×#7631288 #72295852

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

Aliases

Subgroups

2096056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 20 points:

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

Conjugacy classes & character table

488 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)(13,14,17,15)(16,18,20,19), (5,6)(7,8)(14,15)(18,19), (5,6,7,8)(10,12)(16,20)(18,19), (5,6)(7,8)(13,15)(14,17)(16,19)(18,20), (13,16)(14,18)(15,19)(17,20), (5,6,7,8)(9,10)(11,12)(13,16)(14,18)(15,19)(17,20), (5,6)(7,8), (1,2)(3,4));