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C₂×#13358 #498901

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

Aliases

Subgroups

2208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406097);