Finite Group Databasebeta

?

← Prev (#493341) Next (#493343) →

C₂×#12684 #493342

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

Aliases

Subgroups

3154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400538);