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#7623431

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

Aliases

No aliases for this group.

Subgroups

1207 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)(17,18,24,29)(19,25,32,48)(20,35,38,68)(21,27,23,44)(22,40,43,69)(26,50,53,37)(28,39,55,42)(30,56,58,78)(31,47,34,65)(33,62,61,79)(36,67,45,54)(41,51,70,52)(46,71,73,59)(49,60,75,64)(57,77,66,76)(63,72,80,74);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19)(18,25)(20,30)(21,31)(22,33)(23,34)(24,32)(26,46)(27,47)(28,49)(29,48)(35,56)(36,57)(37,59)(38,58)(39,60)(40,62)(41,63)(42,64)(43,61)(44,65)(45,66)(50,71)(51,72)(52,74)(53,73)(54,76)(55,75)(67,77)(68,78)(69,79)(70,80);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(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)(33,63)(34,66)(35,40)(37,42)(39,50)(43,70)(44,52)(47,72)(48,73)(49,76)(55,67)(56,62)(59,64)(60,71)(61,80)(65,74)(68,69)(75,77)(78,79);(2,8)(6,9)(7,16)(14,15)(17,21,24,23)(18,27,29,44)(19,31,32,34)(20,36,38,45)(22,39,43,42)(25,47,48,65)(26,51,53,52)(28,40,55,69)(30,57,58,66)(33,60,61,64)(35,67,68,54)(37,41,50,70)(46,72,73,74)(49,62,75,79)(56,77,78,76)(59,63,71,80);(19,32)(25,48)(30,58)(31,34)(33,61)(46,73)(47,65)(49,75)(56,78)(57,66)(59,71)(60,64)(62,79)(63,80)(72,74)(76,77)

Polycyclic presentation:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530627);