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C₂×#45995 #7702645

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

Aliases

Subgroups

8182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609841);