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#347427

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

Aliases

No aliases for this group.

Subgroups

1922 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=h,b^2=h,d^2=h,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, 254623);