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C₂×#61375 #10576205

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

Aliases

Subgroups

6246 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)(11,12,16,21)(13,22,24,18)(14,26,28,35)(15,20,17,30)(19,31,36,27)(23,38,39,42)(25,34,29,33)(32,41,37,40);(3,5,7,10)(4,8,6,9)(11,13,16,24)(12,18,21,22)(14,23,28,39)(15,29,17,25)(19,32,36,37)(20,34,30,33)(26,42,35,38)(27,41,31,40);(11,14)(12,19)(13,23)(15,27)(16,28)(17,31)(18,32)(20,35)(21,36)(22,37)(24,39)(25,40)(26,30)(29,41)(33,42)(34,38);(3,6,7,4)(5,8,10,9)(13,24)(18,22)(23,39)(25,29)(32,37)(33,34)(38,42)(40,41);(11,15,16,17)(12,20,21,30)(13,25,24,29)(14,27,28,31)(18,33,22,34)(19,35,36,26)(23,40,39,41)(32,42,37,38)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483401);