Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3323 ⋊ C2 |
| Sylow | C47 ⋊ #61201 |
2116 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)(56,59)(57,66)(58,60)(61,70)(62,69)(63,64)(65,68)(67,71);(50,55)(52,54)(56,60)(57,65)(58,70)(59,62)(61,69)(63,66)(64,67)(68,71);(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)(60,62)(61,70)(63,66)(65,67)(68,71);(48,50)(49,52)(51,55)(53,54)(56,58,61,62)(57,63,67,68)(59,69,70,60)(64,66,65,71);(48,49,51,53)(50,54,55,52)(56,57,61,67)(58,68,62,63)(59,66,70,71)(60,65,69,64)Polycyclic presentation:
2^8,47|a^2=f,b^2=h,g^2=h,b^a=bf,c^a=cg,g^a=gh,d^b=df,e^b=eh,g^c=gh,i^c=i^46,e^d=eh,i^e=i^46722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1047542);