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#347428

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

Aliases

No aliases for this group.

Subgroups

1868 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 96 points:

(3,11)(5,16)(7,19)(8,22)(9,17)(12,25)(13,18)(15,27)(20,31)(21,24)(26,29)(30,32)(33,34,39,44)(35,45,49,67)(36,41,52,64)(37,42,54,66)(38,55,58,43)(40,56,61,48)(46,69,73,89)(47,74,76,70)(50,78,80,62)(51,81,84,63)(53,68,57,65)(59,82,86,72)(60,77,87,75)(71,91,93,95)(79,88,83,90)(85,92,96,94);(1,2)(3,7)(4,8)(5,17)(6,10)(9,16)(11,24)(12,20)(13,21)(14,22)(15,28)(18,19)(23,27)(25,31)(26,32)(29,30)(33,35,39,49)(34,40,44,61)(36,46,52,73)(37,47,54,76)(38,56,58,48)(41,59,64,86)(42,60,66,87)(43,67,55,45)(50,71,80,93)(51,82,84,72)(53,77,57,75)(62,85,78,96)(63,89,81,69)(65,70,68,74)(79,94,83,92)(88,91,90,95);(1,3)(2,7)(4,12)(5,18)(6,13)(8,20)(9,24)(10,21)(11,16)(14,26)(15,29)(17,19)(22,32)(23,31)(25,27)(28,30)(33,36)(34,41)(35,46)(37,50)(38,51)(39,52)(40,59)(42,62)(43,63)(44,64)(45,69)(47,71)(48,72)(49,73)(53,79)(54,80)(55,81)(56,82)(57,83)(58,84)(60,85)(61,86)(65,88)(66,78)(67,89)(68,90)(70,91)(74,95)(75,92)(76,93)(77,94)(87,96);(1,4,6,14)(2,8,10,22)(3,12,13,26)(5,15,16,27)(7,20,21,32)(9,23,17,28)(11,25,18,29)(19,30,24,31)(33,37)(34,42)(35,47)(36,50)(38,57)(39,54)(40,60)(41,62)(43,68)(44,66)(45,70)(46,71)(48,77)(49,76)(51,83)(52,80)(53,58)(55,65)(56,75)(59,85)(61,87)(63,90)(64,78)(67,74)(69,91)(72,94)(73,93)(79,84)(81,88)(82,92)(86,96)(89,95)

Polycyclic presentation:

2^9|a^2=h,b^2=h,d^2=i,e^2=h,f^2=i,b^a=be,c^a=cf,d^a=dg,e^a=eh,f^a=fi,e^b=eh,f^b=fi,g^b=ghi,e^c=ei,f^c=fi,g^c=gh,e^d=ehi,f^d=fh

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 254624);