Finite Group Databasebeta

?

← Prev (#494662) Next (#494664) →

C₂×#13075 #494663

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

Aliases

Subgroups

1274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401859);