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C₂×#14108 #514436

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

Aliases

Subgroups

5474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 421632);