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C₂×#33596 #7622951

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

Aliases

Subgroups

2012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 66 points:

(1,2);(3,4,10,16)(5,17,19,36)(6,23,26,56)(7,15,9,13)(8,28,31,40)(11,22,34,20)(12,37,39,25)(14,27,42,30)(18,46,47,66)(21,35,50,62)(24,57,32,41)(29,43,59,38)(33,60,61,52)(44,64,63,49)(45,51,58,53)(48,55,54,65);(3,5,7,20,10,19,9,22)(4,11,13,17,16,34,15,36)(6,18,24,48,26,47,32,54)(8,21,27,51,31,50,30,53)(12,33,38,44,39,61,43,63)(14,35,40,45,42,62,28,58)(23,55,41,46,56,65,57,66)(25,49,29,52,37,64,59,60);(3,6)(4,12)(5,18)(7,24)(8,29)(9,32)(10,26)(11,33)(13,38)(14,41)(15,43)(16,39)(17,44)(19,47)(20,48)(21,52)(22,54)(23,28)(25,30)(27,37)(31,59)(34,61)(35,46)(36,63)(40,56)(42,57)(45,65)(49,53)(50,60)(51,64)(55,58)(62,66);(5,19)(11,34)(17,36)(18,47)(20,22)(21,50)(33,61)(35,62)(44,63)(45,58)(46,66)(48,54)(49,64)(51,53)(52,60)(55,65)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530147);