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#7624339

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

Aliases

No aliases for this group.

Subgroups

1206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 80 points:

(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,24,30)(19,25,35,52)(20,27,38,60)(21,28,23,46)(22,42,45,73)(26,53,57,37)(29,41,61,44)(31,62,32,48)(33,49,39,51)(34,68,70,75)(36,58,40,59)(43,55,72,56)(47,66,54,64)(50,71,79,67)(63,78,65,77)(69,80,74,76);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19)(18,25)(20,32)(21,39)(22,34)(23,33)(24,35)(26,54)(27,48)(28,51)(29,50)(30,52)(31,38)(36,63)(37,66)(40,65)(41,71)(42,68)(43,74)(44,67)(45,70)(46,49)(47,57)(53,64)(55,76)(56,80)(58,78)(59,77)(60,62)(61,79)(69,72)(73,75);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,20)(18,26)(19,31)(21,36)(22,43)(23,40)(24,38)(25,47)(27,42)(28,55)(29,59)(30,57)(32,35)(33,63)(34,69)(37,44)(39,65)(41,53)(45,72)(46,56)(48,75)(49,76)(50,78)(51,80)(52,54)(58,61)(60,73)(62,68)(64,67)(66,71)(70,74)(77,79);(3,11)(6,9)(10,16)(13,15)(17,20)(18,27)(19,32)(21,40)(22,37)(23,36)(24,38)(25,48)(26,42)(28,59)(29,55)(30,60)(31,35)(33,63)(34,66)(39,65)(41,72)(43,44)(45,53)(46,58)(47,75)(49,78)(50,76)(51,77)(52,62)(54,68)(56,61)(57,73)(64,70)(67,74)(69,71)(79,80);(2,8)(6,9)(7,14)(13,15)(17,21,24,23)(18,28,30,46)(19,33,35,39)(20,36,38,40)(22,41,45,44)(25,49,52,51)(26,55,57,56)(27,58,60,59)(29,42,61,73)(31,63,32,65)(34,67,70,71)(37,43,53,72)(47,76,54,80)(48,77,62,78)(50,75,79,68)(64,74,66,69)

Polycyclic presentation:

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

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531535);