Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3131 ⋊ C2 |
| Sylow | C47 ⋊ #60724 |
1874 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)(61,73)(62,75)(63,77)(64,78)(66,82)(67,83)(69,85)(71,84)(72,74)(76,80)(79,81)(86,87);(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)(60,75)(65,82)(68,73)(70,74)(77,80)(78,81)(83,84)(85,87);(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)(56,59,61,71,62,72,58,67)(57,64,63,69,66,79,76,86)(60,74,73,83,75,70,68,84)(65,81,77,87,82,78,80,85);(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)(57,63,66,76)(59,67,72,71)(60,73,75,68)(64,69,79,86)(65,80,82,77)(70,84,74,83)(78,87,81,85);(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)(61,76)(62,66)(64,71)(67,79)(68,77)(70,85)(72,86)(73,80)(74,87)(75,82)(78,84)(81,83)Polycyclic presentation:
2^8,47|b^2=h,c^2=g,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,e^c=eh,i^c=i^46,e^d=eh,i^d=i^461076 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1040037);