Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3083 ⋊ C2 |
| Sylow | C47 ⋊ #61350 |
1746 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)(56,60,61,62)(57,65,66,67)(58,71,70,75)(59,73,74,76)(63,78,68,80)(64,72,79,81)(69,85,84,86)(77,83,82,87);(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)(48,50,51,55)(49,53,52,54)(58,70)(63,68)(69,84)(71,75)(77,82)(78,80)(83,87)(85,86);(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)(57,64)(58,69)(60,73)(61,74)(62,76)(63,77)(65,72)(66,79)(67,81)(68,82)(70,84)(71,85)(75,86)(78,83)(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)(48,49,51,52)(50,54,55,53)(56,58,61,70)(57,63,66,68)(59,69,74,84)(60,75,62,71)(64,77,79,82)(65,80,67,78)(72,87,81,83)(73,86,76,85);(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)(53,54)(56,57,61,66)(58,68,70,63)(59,72,74,81)(60,67,62,65)(64,76,79,73)(69,83,84,87)(71,78,75,80)(77,86,82,85)Polycyclic presentation:
2^8,47|a^2=h,b^2=f,d^2=fh,e^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,i^a=i^46,d^b=df,e^b=eh,i^b=i^46,g^c=gh,i^c=i^46,i^d=i^46791 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1049977);