Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3315 ⋊ C2 |
| Sylow | C47 ⋊ #62012 |
1792 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3008 |
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)(48,50,51,54)(49,53,52,55)(58,69)(63,78)(67,83)(68,70)(76,87)(77,84)(81,86)(82,85);(49,52)(53,55)(56,60,62,61)(57,65,66,74)(58,68,69,70)(59,72,73,75)(63,77,78,84)(64,79,80,71)(67,82,83,85)(76,86,87,81);(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)(56,59)(57,64)(58,67)(60,72)(61,75)(62,73)(63,76)(65,79)(66,80)(68,82)(69,83)(70,85)(71,74)(77,86)(78,87)(81,84);(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)(56,58,62,69)(57,63,66,78)(59,67,73,83)(60,68,61,70)(64,76,80,87)(65,77,74,84)(71,81,79,86)(72,82,75,85);(49,52)(50,54)(56,57)(58,63)(59,71)(60,65)(61,74)(62,66)(64,72)(67,81)(68,77)(69,78)(70,84)(73,79)(75,80)(76,82)(83,86)(85,87)Polycyclic presentation:
2^8,47|b^2=h,d^2=h,e^2=f,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,d^b=df,e^b=eh,i^b=i^46,g^c=gh,i^c=i^46,i^e=i^46716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1062991);