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#7624304

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

Aliases

No aliases for this group.

Subgroups

1215 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)(36,67)(38,68)(39,55)(41,51)(43,66)(45,54)(46,59)(49,62)(52,70)(53,69)(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)(17,19,24,34)(18,25,29,50)(20,30,38,60)(21,31,23,32)(22,33,43,65)(26,46,53,73)(27,47,44,48)(28,49,55,76)(35,56,68,78)(36,57,45,58)(37,59,69,80)(39,61,42,62)(40,63,66,74)(41,64,70,79)(51,71,52,72)(54,75,67,77);(1,4,5,12)(2,7,8,14)(3,10,11,16)(6,13,9,15)(17,20,24,38)(18,26,29,53)(19,30,34,60)(21,36,23,45)(22,41,43,70)(25,46,50,73)(27,51,44,52)(28,54,55,67)(31,57,32,58)(33,64,65,79)(35,66,68,40)(37,39,69,42)(47,71,48,72)(49,75,76,77)(56,74,78,63)(59,61,80,62);(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)(28,40,55,66)(30,57,60,58)(33,61,65,62)(35,67,68,54)(37,41,69,70)(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)(28,40,55,66)(30,58,60,57)(33,62,65,61)(35,67,68,54)(37,41,69,70)(46,72,73,71)(49,74,76,63)(56,75,78,77)(59,79,80,64)

Polycyclic presentation:

2^9|b^2=i,c^2=fi,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, 7531500);