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C₂×#12911 #494168

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

Aliases

Subgroups

628 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401364);