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C₂×#13622 #512697

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

Aliases

Subgroups

784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 419893);