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#263576

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

Aliases

No aliases for this group.

Subgroups

706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Polycyclic presentation:

2^9|a^2=h,b^2=ei,c^2=i,d^2=eh,e^2=h,f^2=i,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fi,g^a=ghi,c^b=cg,f^b=fhi,g^b=gh,d^c=di,f^c=fi,g^c=gh

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 170772);