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C₂×#23498 #6431886

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

Aliases

Subgroups

4966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339082);