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C₂×#35574 #7628957

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

Aliases

Subgroups

9610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536153);