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#7624355

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

Aliases

No aliases for this group.

Subgroups

1213 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)(22,42,45,72)(26,53,56,37)(29,41,61,44)(31,57,32,48)(33,49,39,51)(34,67,69,73)(36,58,40,59)(43,54,71,55)(47,65,75,63)(50,70,78,66)(62,77,64,76)(68,79,80,74);(1,3)(2,6)(4,10)(5,11)(7,13)(8,9)(12,16)(14,15)(17,19,24,35)(18,25,30,52)(20,31,38,32)(21,39,23,33)(22,34,45,69)(26,47,56,75)(27,57,60,48)(28,51,46,49)(29,50,61,78)(36,64,40,62)(37,63,53,65)(41,70,44,66)(42,67,72,73)(43,68,71,80)(54,79,55,74)(58,76,59,77);(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)(28,54)(29,59)(30,56)(32,35)(33,62)(34,68)(37,44)(39,64)(41,53)(45,71)(46,55)(48,73)(49,74)(50,77)(51,79)(52,75)(57,67)(58,61)(60,72)(63,66)(65,70)(69,80)(76,78);(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)(29,54)(30,60)(31,35)(33,62)(34,65)(39,64)(41,71)(43,44)(45,53)(46,58)(47,73)(49,77)(50,74)(51,76)(52,57)(55,61)(56,72)(63,69)(66,80)(67,75)(68,70)(78,79);(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)(26,54,56,55)(27,58,60,59)(29,42,61,72)(31,62,32,64)(34,66,69,70)(37,43,53,71)(47,74,75,79)(48,76,57,77)(50,73,78,67)(63,80,65,68)

Polycyclic presentation:

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

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, 7531551);