Finite Group Databasebeta

?

← Prev (#498815) Next (#498817) →

C₂×#13311 #498816

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

Aliases

Subgroups

1488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406012);