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#7624472

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

Polycyclic presentation:

2^9|a^2=i,b^2=f,c^2=f,d^2=fi,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, 7531668);