Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3255 ⋊ C2 |
| Sylow | C47 ⋊ #62091 |
1776 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)(48,50,51,54)(49,53,52,55)(57,66)(58,71)(64,80)(65,67)(69,85)(70,72)(73,81)(84,86);(49,52)(53,55)(56,60,61,62)(57,65,66,67)(58,70,71,72)(59,74,75,76)(63,78,68,79)(64,73,80,81)(69,84,85,86)(77,87,82,83);(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)(56,59,61,75)(57,64,66,80)(58,69,71,85)(60,74,62,76)(63,77,68,82)(65,73,67,81)(70,84,72,86)(78,87,79,83);(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)(48,49)(50,53)(51,52)(54,55)(56,58)(57,63)(59,69)(60,70)(61,71)(62,72)(64,77)(65,78)(66,68)(67,79)(73,87)(74,84)(75,85)(76,86)(80,82)(81,83);(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)(50,54)(56,57)(58,68)(59,73)(60,67)(61,66)(62,65)(63,71)(64,74)(69,83)(70,78)(72,79)(75,81)(76,80)(77,86)(82,84)(85,87)Polycyclic presentation:
2^8,47|c^2=h,d^2=h,e^2=fh,g^2=h,b^a=bf,c^a=cg,d^a=dh,e^a=ef,g^a=gh,i^a=i^46,d^b=dfh,e^b=eh,i^b=i^46,g^c=gh,i^c=i^46644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1065046);