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C₂×#21599 #6373118

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

Aliases

Subgroups

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280314);