Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3166 ⋊ C2 |
| Sylow | C47 ⋊ #60726 |
1842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 6016 |
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)(56,59)(57,63)(58,68)(60,72)(61,70)(62,77)(64,80)(65,78)(66,82)(67,71)(69,84)(73,87)(74,83)(75,86)(76,79)(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)(48,50,51,54)(49,53,52,55)(59,70)(63,78)(68,71)(72,83)(77,79)(80,87)(82,85)(84,86);(56,58,60,69,61,67,74,75)(57,62,64,66,65,76,73,81)(59,71,72,86,70,68,83,84)(63,79,80,85,78,77,87,82);(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)(49,52)(53,55)(58,67)(59,70)(62,76)(63,78)(66,81)(69,75)(72,83)(80,87);(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)(48,49)(50,53)(51,52)(54,55)(56,57,61,65)(58,66,67,81)(59,63,70,78)(60,73,74,64)(62,75,76,69)(68,82,71,85)(72,87,83,80)(77,86,79,84)Polycyclic presentation:
2^8,47|a^2=h,c^2=g,d^2=f,g^2=h,b^a=bf,c^a=cg,g^a=gh,i^a=i^46,c^b=ch,e^b=eh,i^b=i^46,e^c=eh,e^d=eh,i^d=i^46794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1040062);