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#7623424

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

Aliases

No aliases for this group.

Subgroups

1200 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)(19,25,32,47)(20,36,39,68)(21,29,23,27)(22,41,44,54)(26,51,53,38)(28,40,56,43)(31,58,59,78)(33,50,35,48)(34,64,62,75)(37,69,45,55)(42,57,70,52)(46,71,72,61)(49,63,74,66)(60,79,67,76)(65,77,80,73);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19)(18,25)(20,31)(21,33)(22,34)(23,35)(24,32)(26,46)(27,48)(28,49)(29,50)(30,47)(36,58)(37,60)(38,61)(39,59)(40,63)(41,64)(42,65)(43,66)(44,62)(45,67)(51,71)(52,73)(53,72)(54,75)(55,76)(56,74)(57,77)(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)(19,31)(21,37)(22,42)(23,45)(24,39)(25,46)(27,52)(28,55)(29,57)(30,53)(32,59)(33,60)(34,65)(35,67)(36,41)(38,43)(40,51)(44,70)(47,72)(48,73)(49,76)(50,77)(54,68)(56,69)(58,64)(61,66)(62,80)(63,71)(74,79)(75,78);(2,8)(6,9)(7,16)(14,15)(19,32)(25,47)(31,59)(33,35)(34,62)(46,72)(48,50)(49,74)(58,78)(60,67)(61,71)(63,66)(64,75)(65,80)(73,77)(76,79);(17,21,24,23)(18,27,30,29)(19,33,32,35)(20,37,39,45)(22,40,44,43)(25,48,47,50)(26,52,53,57)(28,54,56,41)(31,60,59,67)(34,63,62,66)(36,55,68,69)(38,42,51,70)(46,73,72,77)(49,75,74,64)(58,76,78,79)(61,65,71,80)

Polycyclic presentation:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530620);