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C₂×#1085142 #72279140

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

Aliases

Subgroups

56287 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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