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C₂×#33393 #7622512

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

Aliases

Subgroups

3892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7529708);