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C₂²×#34265 #72302754

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

Aliases

Subgroups

144781 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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