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C₂×#72233695 #72286913

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

Aliases

Subgroups

2832014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

(3,4)(5,6)(7,8)(9,10)(12,14)(15,16)(17,19)(18,21)(20,22);(15,16)(17,20)(18,21)(19,22);(11,12,13,14)(15,17)(16,19)(18,22)(20,21);(1,2);(4,6)(8,9);(8,9)(15,17)(16,20)(18,22)(19,21);(3,4)(5,6)(7,9,10,8)(15,16)(17,19)(18,21)(20,22)

Conjugacy classes & character table

344 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)(12,14)(15,16)(17,19)(18,21)(20,22), (15,16)(17,20)(18,21)(19,22), (11,12,13,14)(15,17)(16,19)(18,22)(20,21), (1,2), (4,6)(8,9), (8,9)(15,17)(16,20)(18,22)(19,21), (3,4)(5,6)(7,9,10,8)(15,16)(17,19)(18,21)(20,22));