Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3203 ⋊ C2 |
| Sylow | C47 ⋊ #61626 |
2046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 87 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)(49,53)(52,54)(56,60,62,61)(57,65,66,74)(58,69,70,68)(59,72,73,75)(63,78,79,77)(64,80,81,71)(67,84,85,83)(76,82,87,86);(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)(50,55)(52,54)(56,60,62,61)(57,65,66,74)(58,68,70,69)(59,72,73,75)(63,77,79,78)(64,80,81,71)(67,83,85,84)(76,86,87,82);(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)(56,59)(57,64)(58,67)(60,72)(61,75)(62,73)(63,76)(65,80)(66,81)(68,83)(69,84)(70,85)(71,74)(77,86)(78,82)(79,87);(48,50)(49,52)(51,55)(53,54)(56,58,62,70)(57,63,66,79)(59,67,73,85)(60,68,61,69)(64,76,81,87)(65,77,74,78)(71,82,80,86)(72,83,75,84);(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)(50,54)(51,53)(52,55)(56,57)(58,63)(59,71)(60,65)(61,74)(62,66)(64,72)(67,82)(68,77)(69,78)(70,79)(73,80)(75,81)(76,83)(84,87)(85,86)Polycyclic presentation:
2^8,47|b^2=h,d^2=h,e^2=h,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,i^a=i^46,d^b=df,e^b=eh,g^c=gh,i^c=i^46,i^d=i^46647 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1055554);