Finite Group Databasebeta

?

← Prev (#7501829) Next (#7501831) →

#7501830

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

Aliases

No aliases for this group.

Subgroups

2274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 72 points:

(1,2)(3,5)(4,6)(7,8)(9,10)(11,17)(12,28)(13,34)(14,20)(15,21)(16,22)(18,32)(19,36)(23,49)(24,52)(25,40)(26,41)(27,42)(29,38)(30,44)(31,45)(33,48)(35,47)(37,46)(39,53)(43,51)(50,62)(54,65)(55,64)(56,63)(57,59)(58,66)(60,68)(61,67)(69,70)(71,72);(1,3,5,2)(4,7,8,6)(9,11,16,27)(10,17,22,42)(12,29,33,56)(13,24,37,55)(14,26,15,25)(18,43,45,49)(19,39,47,65)(20,41,21,40)(23,32,51,31)(28,38,48,63)(30,58,60,70)(34,52,46,64)(35,54,36,53)(44,66,68,69)(50,61,71,59)(57,62,67,72);(1,4,5,8)(2,6,3,7)(9,12)(10,18)(11,23)(13,30)(14,31)(15,32)(16,33)(17,38)(19,44)(20,28)(21,48)(22,45)(24,50)(25,29)(26,56)(27,51)(34,57)(35,59)(36,61)(37,60)(39,62)(40,43)(41,49)(42,63)(46,67)(47,68)(52,69)(53,58)(54,70)(55,71)(64,66)(65,72);(2,3)(6,7)(9,13)(10,19)(11,24)(12,30)(14,35)(15,36)(16,37)(17,39)(18,44)(20,34)(21,46)(22,47)(23,50)(25,53)(26,54)(27,55)(28,57)(29,58)(31,59)(32,61)(33,60)(38,62)(40,64)(41,52)(42,65)(43,66)(45,68)(48,67)(49,69)(51,71)(56,70)(63,72);(9,14,16,15)(10,20,22,21)(11,25,27,26)(12,31,33,32)(13,35,37,36)(17,40,42,41)(18,28,45,48)(19,34,47,46)(23,29,51,56)(24,53,55,54)(30,59,60,61)(38,43,63,49)(39,64,65,52)(44,57,68,67)(50,58,71,70)(62,66,72,69)

Polycyclic presentation:

2^9|b^2=fi,c^2=f,e^2=i,g^2=i,h^2=i,b^a=bf,c^a=cg,d^a=dfg,g^a=gi,c^b=ch,d^b=df,e^b=ei,h^b=hi,g^c=gi,h^c=hi,g^d=gi

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7409026);