Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C47×#568 ⋊ C2 |
| Sylow | C47 ⋊ #60088 |
4810 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)(53,60)(58,72)(59,73)(61,68)(62,75)(71,82)(74,80)(76,83);(55,66)(59,73)(63,77)(67,79)(71,82)(74,80)(76,83)(78,81);(52,55)(53,59)(54,63)(56,67)(57,66)(58,71)(60,73)(61,74)(62,76)(64,78)(65,77)(68,80)(69,81)(70,79)(72,82)(75,83);(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)(52,54,57,65)(53,58,60,72)(55,63,66,77)(56,69,70,64)(59,71,73,82)(61,75,68,62)(67,81,79,78)(74,83,80,76);(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)(54,62)(55,59)(56,68)(57,60)(58,64)(61,70)(63,76)(65,75)(66,73)(67,80)(69,72)(71,78)(74,79)(77,83)(81,82)Polycyclic presentation:
2^8,47|a^2=g,b^2=h,f^2=h,b^a=bf,e^a=eh,f^a=fh,i^a=i^46,f^b=fh,i^b=i^46,d^c=dh1646 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033146);