Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C47×#462 ⋊ C2 |
| Sylow | C47 ⋊ #61097 |
2654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 6016 |
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)(52,55)(53,60)(54,63)(56,68)(57,66)(58,73)(59,74)(61,67)(62,77)(64,80)(65,78)(69,81)(70,76)(71,83)(72,79)(75,82);(52,54,57,65)(53,59,61,75)(55,63,66,78)(56,71,69,64)(58,72,70,62)(60,74,67,82)(68,83,81,80)(73,79,76,77);(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)(55,66)(60,67)(63,78)(68,81)(73,76)(74,82)(77,79)(80,83);(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)(52,53,57,61)(54,62,65,72)(55,67,66,60)(56,70,69,58)(59,71,75,64)(63,79,78,77)(68,73,81,76)(74,80,82,83);(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)(53,58)(55,66)(56,69)(59,72)(60,76)(61,70)(62,75)(63,78)(64,71)(67,73)(74,77)(79,82)Polycyclic presentation:
2^8,47|b^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,e^b=eh,f^b=fh,i^b=i^46,e^c=eh,i^c=i^46,f^d=fh929 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045742);