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C₂×#13447 #499163

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

Aliases

Subgroups

1016 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406359);