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C₂×#10576108 #72235100

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

Aliases

Subgroups

118049 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((1,2), (9,15)(10,17)(13,20)(14,19)(16,21)(18,22), (3,4)(5,6), (8,12)(9,16)(14,19)(15,21), (4,6)(7,8,11,12)(9,13,16,18)(10,14,17,19)(15,20,21,22), (7,9,10,15,11,16,17,21)(8,13,14,20,12,18,19,22), (8,12)(13,18)(14,19)(20,22));