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C₂×#13071 #494654

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

Aliases

Subgroups

1274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401850);