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C₂×#13406 #499044

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

Aliases

Subgroups

1052 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406240);