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C₂×#33340 #7622437

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

Aliases

Subgroups

3924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 66 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529633);