Finite Group Databasebeta

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C₂²×#62818 #72299711

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

Aliases

Subgroups

516797 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((7,11)(10,12)(13,14)(15,18)(16,17)(19,20), (14,17)(18,20), (6,9)(10,12)(15,19)(18,20), (6,9)(10,12)(13,15)(14,18)(16,19)(17,20), (5,6,8,9)(7,12,11,10)(13,14)(15,20)(16,17)(18,19), (5,7)(6,10)(8,11)(9,12), (3,4), (1,2)(3,4));