Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3127 ⋊ C2 |
| Sylow | C47 ⋊ #60598 |
2010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6016 |
A minimal faithful permutation representation — 5 generators on 87 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)(56,59,61,71)(57,64,66,80)(58,67,69,70)(60,72,73,85)(62,75,77,79)(63,78,65,81)(68,82,83,84)(74,86,76,87);(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)(48,50,51,54)(49,53,52,55)(59,71)(64,80)(67,70)(72,85)(75,79)(78,81)(82,84)(86,87);(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)(57,63)(60,73)(62,74)(64,78)(65,66)(68,83)(72,85)(75,86)(76,77)(79,87)(80,81)(82,84);(49,52)(53,55)(56,58,61,69)(57,62,66,77)(59,70,71,67)(60,68,73,83)(63,74,65,76)(64,79,80,75)(72,84,85,82)(78,87,81,86);(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)(50,53)(51,52)(54,55)(56,57)(58,62)(59,64)(60,63)(61,66)(65,73)(67,75)(68,74)(69,77)(70,79)(71,80)(72,78)(76,83)(81,85)(82,86)(84,87)Polycyclic presentation:
2^8,47|b^2=h,d^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,g^a=gh,i^a=i^46,e^b=eh,g^c=gh,i^c=i^46,e^d=eh,i^d=i^46,i^e=i^46797 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1038688);