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C₂×#33693 #7623142

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

Aliases

Subgroups

1467 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530338);