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C₂×#59273 #7666188

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

Aliases

Subgroups

9494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573384);