Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3307 ⋊ C2 |
| Sylow | C47 ⋊ #62166 |
1750 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 79 points:
(1,2)(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)(48,51,52,60)(49,54,55,59)(50,58,57,63)(53,61,56,62)(65,71)(66,74)(70,72)(75,79);(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)(50,57)(53,56)(58,63)(61,62)(66,74)(69,73)(75,79)(77,78);(65,70)(68,76)(69,77)(71,72)(73,78)(75,79);(48,50)(49,53)(51,58)(52,57)(54,61)(55,56)(59,62)(60,63)(64,66,67,74)(65,69,71,73)(68,75,76,79)(70,77,72,78);(48,49,52,55)(50,56,57,53)(51,59,60,54)(58,61,63,62)(64,65)(66,73)(67,71)(68,70)(69,74)(72,76)(75,78)(77,79)Polycyclic presentation:
2^8,47|a^2=fh,b^2=h,e^2=fh,g^2=h,b^a=bf,c^a=cg,e^a=ef,g^a=gh,d^b=df,e^b=eh,g^c=gh,i^d=i^46,i^e=i^46716 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1066551);