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C₂×#33540 #7622846

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

Aliases

Subgroups

3806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530042);