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C₂×#59407 #7666154

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

Aliases

Subgroups

9998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573350);