Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C47 ⋊ #60109 |
2694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 67 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(53,59)(57,64)(58,65)(63,67);(54,60)(58,65)(61,66)(63,67);(52,54)(53,58)(55,61)(56,60)(57,63)(59,65)(62,66)(64,67);(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)(52,53,55,57,56,59,62,64)(54,58,61,63,60,65,66,67);(48,49,50,51)(53,57)(55,62)(58,63)(59,64)(61,66)(65,67)Polycyclic presentation:
2^8,47|a^2=g,b^2=f,f^2=h,b^a=bf,f^a=fh,e^b=eh,i^b=i^46,d^c=dh1646 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1033252);