Finite Group Databasebeta

?

← Prev (#7622843) Next (#7622845) →

C₂×#33538 #7622844

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

Aliases

Subgroups

3832 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)(7,13)(8,28)(9,15)(10,16)(11,20)(12,25)(14,30)(18,46)(19,44)(21,45)(23,38)(24,55)(26,42)(27,41)(29,34)(31,40)(32,39)(33,60)(35,59)(36,51)(37,58)(43,49)(47,65)(48,52)(50,63)(53,57)(54,64)(56,62)(61,66);(3,5)(4,11)(6,18)(7,19)(8,29)(9,32)(10,21)(12,33)(13,34)(14,39)(15,35)(16,36)(17,28)(20,30)(22,52)(23,47)(24,56)(25,49)(26,50)(27,51)(31,59)(37,63)(38,62)(40,45)(41,44)(42,61)(43,53)(46,55)(48,57)(54,66)(58,60)(64,65);(3,6)(4,12)(5,18)(7,23)(8,24)(9,25)(10,26)(11,33)(13,22)(14,37)(15,42)(16,38)(17,43)(19,47)(20,48)(21,50)(27,54)(28,53)(29,56)(30,57)(31,58)(32,49)(34,52)(35,61)(36,62)(39,63)(40,64)(41,55)(44,46)(45,65)(51,66)(59,60);(3,7,10,9)(4,13,16,15)(5,19,21,32)(6,23,26,25)(8,27,31,30)(11,34,36,35)(12,22,38,42)(14,28,41,40)(17,44,45,39)(18,47,50,49)(20,29,51,59)(24,54,58,57)(33,52,62,61)(37,53,55,64)(43,46,65,63)(48,56,66,60)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530040);