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C₂×#25485 #6446158

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

Aliases

Subgroups

2272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6353354);