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C₂²×#62912 #72278670

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

Aliases

Subgroups

517517 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

292 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((5,6)(7,10)(8,12)(9,11)(13,14)(15,17)(16,18)(19,20), (13,14,16,18)(15,17,19,20), (5,7,9,12)(6,10,11,8)(15,19)(17,20), (7,12)(8,10)(13,15)(14,17)(16,19)(18,20), (5,8)(6,7)(9,10)(11,12)(13,14)(15,17)(16,18)(19,20), (5,6)(7,8)(9,11)(10,12)(13,14)(15,17)(16,18)(19,20), (3,4), (1,2)(3,4));