Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C47×#3041 ⋊ C2 |
| Sylow | C47 ⋊ #60423 |
2890 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1504 |
A minimal faithful permutation representation — 5 generators on 67 points:
(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)(53,59)(57,65)(58,60)(64,66);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,61)(57,65)(62,67)(64,66);(53,58)(55,63)(57,64)(59,60)(62,67)(65,66);(48,49,50,51)(52,54)(53,57)(55,62)(56,61)(58,64)(59,65)(60,66)(63,67);(49,51)(52,53)(54,57)(55,58)(56,59)(60,63)(61,65)(62,64)(66,67)Polycyclic presentation:
2^8,47|b^2=f,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,d^b=dh,g^c=gh,i^e=i^46794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1036525);