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C₂×#33671 #7623081

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

Aliases

Subgroups

1576 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)(13,23)(14,20)(15,21)(16,19)(17,31)(18,25)(22,30)(24,38)(26,37)(27,33)(28,35)(29,36)(32,41)(34,40)(39,42);(4,7)(8,10)(11,13,15,25)(12,18,21,23)(14,24,17,27)(16,26,29,41)(19,32,36,37)(20,33,31,38)(22,34,35,39)(28,40,30,42);(12,19)(14,17)(16,30)(18,32)(20,22)(21,36)(23,37)(24,27)(26,42)(28,29)(31,35)(33,34)(38,39)(40,41);(3,5,6,9)(4,8,7,10)(11,14,15,17)(12,20,21,31)(13,24,25,27)(16,28,29,30)(18,33,23,38)(19,35,36,22)(26,40,41,42)(32,39,37,34)

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, 7530277);