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#7054936

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

Aliases

No aliases for this group.

Subgroups

2004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 72 points:

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

Polycyclic presentation:

2^9|a^2=i,c^2=hi,e^2=i,f^2=i,g^2=i,b^a=bf,c^a=cg,e^a=eh,f^a=fi,g^a=gi,c^b=ch,d^b=df,e^b=eh,f^b=fi,d^c=dh,e^c=ei,g^c=gi,f^d=fi

Conjugacy classes & character table

62 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6962132);