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C₂×#33617 #7622988

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

Aliases

Subgroups

1908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530184);