Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C47×#477 ⋊ C2 |
| Sylow | C47 ⋊ #60600 |
2046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 6016 |
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)(56,60,61,57)(58,67,68,63)(59,64,62,69)(65,66,71,70);(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)(56,59,61,62)(57,64,60,69)(58,66,68,70)(63,71,67,65);(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)(56,58,61,68)(57,63,60,67)(59,66,62,70)(64,71,69,65);(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)(57,60)(63,67)(64,69)(65,71);(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)(56,57,61,60)(58,65,68,71)(59,64,62,69)(63,70,67,66)Polycyclic presentation:
2^8,47|a^2=h,c^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,i^b=i^46,g^c=gh,i^c=i^46,e^d=eh,i^d=i^46935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1038726);