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C₂×#33740 #7623233

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

Aliases

Subgroups

1468 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)(13,21)(14,22)(15,25)(17,27)(19,28)(20,32)(23,37)(24,35)(26,36)(29,38)(30,42)(31,41)(33,34)(39,40);(4,7)(8,10)(11,12,16,18)(13,17,24,29)(14,19,26,31)(15,20,25,32)(21,27,35,38)(22,28,36,41)(23,30,33,39)(34,40,37,42);(11,13,22,34,15,23,26,35,16,24,36,37,25,33,14,21)(12,17,28,40,20,30,31,38,18,29,41,42,32,39,19,27);(3,5,6,9)(4,8,7,10)(12,18)(17,29)(19,31)(20,32)(27,38)(28,41)(30,39)(40,42)

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, 7530429);