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C₂²×#612433 #72289264

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

Aliases

Subgroups

8435028 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

464 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((5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20), (9,10)(11,12)(17,18)(19,20), (13,14)(15,16)(17,18,19,20), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20), (5,6)(7,8)(9,10)(11,12)(13,14)(15,16), (3,4), (1,2)(3,4));