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C₂×#11117 #357783

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

Aliases

Subgroups

2826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264979);