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C₂×#37795 #7635035

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

Aliases

Subgroups

7574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542231);