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C₂×#33414 #7622540

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

Aliases

Subgroups

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529736);