Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3076 ⋊ C2 |
| Sylow | C47 ⋊ #60595 |
2014 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)(56,60)(57,65)(58,68)(59,70)(61,72)(62,73)(63,77)(64,78)(66,81)(67,82)(69,83)(71,85)(74,80)(75,84)(76,86)(79,87);(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)(60,73)(65,81)(68,72)(70,85)(77,80)(78,87)(82,84)(83,86);(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)(56,59,62,71)(57,64,66,79)(58,67,61,75)(60,70,73,85)(63,76,74,69)(65,78,81,87)(68,82,72,84)(77,86,80,83);(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)(49,52)(53,55)(56,58,62,61)(57,63,66,74)(59,67,71,75)(60,72,73,68)(64,76,79,69)(65,80,81,77)(70,84,85,82)(78,83,87,86);(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)(48,49)(50,53)(51,52)(54,55)(56,57)(58,63)(59,69)(60,65)(61,74)(62,66)(64,67)(68,77)(70,83)(71,76)(72,80)(73,81)(75,79)(78,82)(84,87)(85,86)Polycyclic presentation:
2^8,47|b^2=h,c^2=h,d^2=f,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, 1038635);