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C₂×#59421 #7666406

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

Aliases

Subgroups

8682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573602);