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C₂×#26930 #6443521

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

Aliases

Subgroups

2976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 6350717);