Finite Group Databasebeta

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#27091218

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

1724 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 79 points:

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

Polycyclic presentation:

2^8,47|b^2=h,d^2=h,e^2=f,g^2=h,b^a=bf,c^a=cg,d^a=df,g^a=gh,i^a=i^46,c^b=cfh,d^b=dh,i^b=i^46,g^c=gh,i^c=i^46,e^d=eh,i^d=i^46,i^e=i^46

Conjugacy classes & character table

644 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1044508);