Finite Group Databasebeta

?

← Prev (#7623847) Next (#7623849) →

#7623848

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

Aliases

No aliases for this group.

Subgroups

1258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531044);