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#7054970

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

Aliases

No aliases for this group.

Subgroups

2001 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)(11,23,28,49)(12,29,33,48)(13,19,38,47)(14,20,15,21)(17,26,41,27)(18,31,43,32)(24,39,56,69)(25,52,59,44)(30,61,35,67)(34,65,58,40)(36,46,37,50)(42,63,45,64)(51,54,60,55)(53,68,57,70)(62,72,66,71);(1,2)(3,7)(4,6)(5,8)(9,11)(10,17)(12,24)(13,34)(14,26)(15,27)(16,28)(18,39)(19,44)(20,23)(21,49)(22,41)(25,37)(29,60)(30,62)(31,54)(32,55)(33,56)(35,66)(36,59)(38,58)(40,46)(42,71)(43,69)(45,72)(47,52)(48,51)(50,65)(53,63)(57,64)(61,70)(67,68);(1,3,4,8)(2,5,6,7)(9,12,16,33)(10,18,22,43)(11,24,28,56)(13,35,38,30)(14,32,15,31)(17,39,41,69)(19,45,47,42)(20,48,21,29)(23,51,49,60)(25,57,59,53)(26,55,27,54)(34,66,58,62)(36,63,37,64)(40,70,65,68)(44,72,52,71)(46,61,50,67);(3,8)(5,7)(9,13,16,38)(10,19,22,47)(11,25,28,59)(12,30,33,35)(14,36,15,37)(17,40,41,65)(18,42,43,45)(20,46,21,50)(23,52,49,44)(24,53,56,57)(26,34,27,58)(29,61,48,67)(31,63,32,64)(39,68,69,70)(51,72,60,71)(54,66,55,62);(2,6)(5,7)(9,14,16,15)(10,20,22,21)(11,26,28,27)(12,31,33,32)(13,36,38,37)(17,23,41,49)(18,29,43,48)(19,46,47,50)(24,54,56,55)(25,34,59,58)(30,63,35,64)(39,60,69,51)(40,52,65,44)(42,61,45,67)(53,66,57,62)(68,71,70,72)

Polycyclic presentation:

2^9|a^2=i,c^2=hi,d^2=i,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=dhi,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, 6962166);