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C₂×#61269 #10576595

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

Aliases

Subgroups

6414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 42 points:

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

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, 10483791);