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#7624478

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

Aliases

No aliases for this group.

Subgroups

1222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|b^2=f,c^2=fi,d^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,d^b=dfi,e^b=ei,g^c=gh,h^c=hi

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531674);