Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#135×C47 ⋊ C2 |
| Sylow | C47 ⋊ #60536 |
2192 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 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)(56,59,61,60)(57,63,64,68)(58,66,67,69)(62,70,71,65);(48,50,51,54)(49,53,52,55);(56,58)(57,62)(59,66)(60,69)(61,67)(63,70)(64,71)(65,68);(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)(49,52)(53,55);(48,49)(50,53)(51,52)(54,55)(56,57)(58,65)(59,63)(60,68)(61,64)(62,66)(67,70)(69,71)Polycyclic presentation:
2^8,47|d^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,g^a=gh,i^b=i^46,g^c=gh1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1037664);