Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3039 ⋊ C2 |
| Sylow | C47 ⋊ #61224 |
2020 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)(56,60,62,75)(57,65,66,73)(58,68,61,74)(59,71,72,86)(63,78,76,81)(64,79,80,87)(67,82,70,84)(69,83,77,85);(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)(50,55)(52,54)(60,75)(65,73)(68,74)(71,86)(78,81)(79,87)(82,84)(83,85);(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)(56,59,62,72)(57,64,66,80)(58,67,61,70)(60,71,75,86)(63,77,76,69)(65,79,73,87)(68,82,74,84)(78,85,81,83);(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)(48,50)(49,52)(51,55)(53,54)(56,58,62,61)(57,63,66,76)(59,70,72,67)(60,74,75,68)(64,69,80,77)(65,81,73,78)(71,82,86,84)(79,85,87,83);(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)(48,49,51,53)(50,54,55,52)(56,57)(58,63)(59,69)(60,73)(61,76)(62,66)(64,67)(65,75)(68,81)(70,80)(71,85)(72,77)(74,78)(79,84)(82,87)(83,86)Polycyclic presentation:
2^8,47|a^2=f,b^2=h,c^2=h,e^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,i^a=i^46,c^b=ch,d^b=df,e^b=eh,i^b=i^46,g^c=gh,i^c=i^46,e^d=eh,i^d=i^46788 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1047973);