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C₂²×#62832 #72280301

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

Aliases

Subgroups

548221 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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