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#7624301

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

Aliases

No aliases for this group.

Subgroups

1217 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)(19,25)(20,35)(21,27)(22,40)(23,44)(24,29)(26,37)(28,42)(30,56)(31,47)(32,48)(33,63)(34,50)(36,66)(38,67)(39,55)(41,51)(43,69)(45,54)(46,59)(49,62)(52,70)(53,68)(57,77)(58,75)(60,78)(61,76)(64,71)(65,74)(72,79)(73,80);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19)(18,25)(20,30)(21,31)(22,33)(23,32)(24,34)(26,46)(27,47)(28,49)(29,50)(35,56)(36,57)(37,59)(38,60)(39,61)(40,63)(41,64)(42,62)(43,65)(44,48)(45,58)(51,71)(52,72)(53,73)(54,75)(55,76)(66,77)(67,78)(68,80)(69,74)(70,79);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,20)(18,26)(19,30)(21,36)(22,41)(23,45)(24,38)(25,46)(27,51)(28,54)(29,53)(31,57)(32,58)(33,64)(34,60)(35,40)(37,42)(39,68)(43,70)(44,52)(47,71)(48,72)(49,75)(50,73)(55,66)(56,63)(59,62)(61,80)(65,79)(67,69)(74,78)(76,77);(3,11)(6,9)(10,16)(13,15)(17,21,24,23)(18,27,29,44)(19,31,34,32)(20,36,38,45)(22,39,43,42)(25,47,50,48)(26,51,53,52)(28,40,55,69)(30,57,60,58)(33,61,65,62)(35,66,67,54)(37,41,68,70)(46,71,73,72)(49,63,76,74)(56,77,78,75)(59,64,80,79);(2,8)(6,9)(7,14)(13,15)(17,21,24,23)(18,27,29,44)(19,32,34,31)(20,36,38,45)(22,39,43,42)(25,48,50,47)(26,51,53,52)(28,40,55,69)(30,58,60,57)(33,62,65,61)(35,66,67,54)(37,41,68,70)(46,72,73,71)(49,74,76,63)(56,75,78,77)(59,79,80,64)

Polycyclic presentation:

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

Conjugacy classes & character table

71 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531497);