Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4 |
No aliases for this group.
| Fitting | C47×#2873 ⋊ C2 |
| Sylow | C47 ⋊ C4×#568 |
3250 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 67 points:
(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)(53,58)(57,63)(59,65)(64,67);(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)(54,60)(57,63)(61,66)(64,67);(52,54)(53,57)(55,61)(56,60)(58,63)(59,64)(62,66)(65,67);(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)(48,49,50,51);(52,53,55,59,56,58,62,65)(54,57,61,64,60,63,66,67)Polycyclic presentation:
2^8,47|a^2=f,b^2=g,f^2=h,e^a=eh,i^b=i^46,d^c=dh,i^d=i^461700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1032984);