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C₂×#33482 #7622653

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

Aliases

Subgroups

1432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 42 points:

(1,2);(3,4)(5,8)(6,7)(9,10)(11,12,14,18,15,19,24,30,16,20,25,31,26,32,36,40)(13,17,22,28,23,29,35,39,21,27,33,37,34,38,41,42);(4,7)(8,10);(11,13,14,22,15,23,24,35,16,21,25,33,26,34,36,41)(12,17,18,28,19,29,30,39,20,27,31,37,32,38,40,42);(3,5,6,9)(4,8,7,10)(13,21)(17,27)(22,33)(23,34)(28,37)(29,38)(35,41)(39,42)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529849);