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C₂×#33385 #7622502

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529698);