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C₂×#30575 #7501170

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

Aliases

Subgroups

3034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7408366);