Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C47×#3141 ⋊ C2 |
| Sylow | C47 ⋊ #60618 |
2170 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 71 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)(56,60,62,61)(57,65,67,66)(58,59,68,69)(63,71,70,64);(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)(58,68)(59,69)(63,70)(64,71);(49,53)(52,55)(56,59,60,68,62,69,61,58)(57,64,66,70,67,71,65,63);(48,50,51,54)(49,52,53,55)(56,58,61,69,62,68,60,59)(57,63,65,71,67,70,66,64);(48,49)(50,52)(51,53)(54,55)(56,57)(58,64)(59,63)(60,65)(61,66)(62,67)(68,71)(69,70)Polycyclic presentation:
2^8,47|b^2=g,c^2=f,e^2=h,f^2=h,g^2=h,b^a=bf,c^a=cg,f^a=fh,g^a=gh,d^b=dh,d^c=dh,i^d=i^46,i^e=i^46800 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1038871);