Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C47×#2957 ⋊ C2 |
| Sylow | C47 ⋊ #60182 |
2628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1504 |
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)(49,57)(55,69)(56,71)(58,66)(59,70)(68,78)(72,76)(73,79);(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)(51,63)(56,71)(60,74)(64,65)(68,78)(72,76)(73,79)(75,77);(48,51,53,65,54,63,52,64)(49,56,58,72,57,71,66,76)(50,60,61,75,62,74,67,77)(55,68,70,79,69,78,59,73);(48,50)(49,55)(51,60)(52,67)(53,61)(54,62)(56,68)(57,69)(58,70)(59,66)(63,74)(64,77)(65,75)(71,78)(72,79)(73,76);(48,49,53,58,54,57,52,66)(50,59,61,55,62,70,67,69)(51,56,65,72,63,71,64,76)(60,73,75,68,74,79,77,78)Polycyclic presentation:
2^8,47|a^2=g,c^2=g,f^2=h,g^2=h,b^a=bf,e^a=eh,f^a=fh,f^b=fh,d^c=dh,i^d=i^46,i^e=i^461094 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033893);