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C₂×#1977 #21245

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

Aliases

Subgroups

783 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14233);