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#332032

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

Aliases

No aliases for this group.

Subgroups

476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=h,b^2=h,c^2=i,d^2=h,e^2=h,f^2=i,g^2=hi,b^a=be,c^a=cf,d^a=def,e^a=eh,f^a=fi,g^a=gh,c^b=cg,d^b=de,e^b=eh,f^b=fh,g^b=ghi,f^c=fi,g^c=ghi,e^d=eh,f^d=fi

Conjugacy classes & character table

41 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 239228);