Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C47×#3399 ⋊ C2 |
| Sylow | C47 ⋊ #61402 |
2244 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 63 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)(57,61)(60,62);(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)(48,51,52,50)(49,54,53,55);(48,50,52,51)(49,54,53,55)(57,60)(58,63)(61,62);(48,49,52,53)(50,54,51,55);(49,53)(54,55)(56,57)(58,60)(59,61)(62,63)Polycyclic presentation:
2^8,47|b^2=f,c^2=f,d^2=f,g^2=h,b^a=bf,c^a=cg,e^a=eh,g^a=gh,d^b=df,g^c=gh,i^d=i^46,i^e=i^46722 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1050619);