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C₂×#47847 #7703145

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

Aliases

Subgroups

10228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7610341);