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C₂×#34301 #7625613

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

Aliases

Subgroups

8302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532809);