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C₂×#12827 #493793

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

Aliases

Subgroups

1012 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400989);