Finite Group Databasebeta

?

← Prev (#493541) Next (#493543) →

C₂×#12745 #493542

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

Aliases

Subgroups

3142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400738);