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C₂×#24608 #6453128

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

Aliases

Subgroups

2740 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6360324);