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C₂×#12829 #493797

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

Aliases

Subgroups

1018 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400993);