Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C47×#3058 ⋊ C2 |
| Sylow | C47 ⋊ #61054 |
2710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 83 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)(53,62)(59,75)(60,70)(61,78)(63,73)(74,83)(76,79)(77,80);(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)(52,56,58,69)(53,61,62,78)(54,65,66,82)(55,67,57,72)(59,74,75,83)(60,76,70,79)(63,80,73,77)(64,81,71,68);(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)(49,51)(52,55,58,57)(53,60,62,70)(54,64,66,71)(56,67,69,72)(59,73,75,63)(61,76,78,79)(65,81,82,68)(74,77,83,80);(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)(52,54,58,66)(53,59,62,75)(55,64,57,71)(56,68,69,81)(60,73,70,63)(61,77,78,80)(65,72,82,67)(74,76,83,79);(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)(54,63)(55,60)(56,61)(57,70)(58,62)(59,64)(65,80)(66,73)(67,76)(68,83)(69,78)(71,75)(72,79)(74,81)(77,82)Polycyclic presentation:
2^8,47|b^2=h,c^2=h,d^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,i^a=i^46,d^b=df,f^b=fh,i^b=i^46,i^c=i^46,f^d=fh,i^d=i^46794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1044965);