Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C47×#2956 ⋊ C2 |
| Sylow | C47 ⋊ #61110 |
2684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 752 |
A minimal faithful permutation representation — 5 generators on 63 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)(49,57)(50,55)(56,60)(58,62);(48,51)(49,56)(50,58)(52,59)(53,54)(55,62)(57,60)(61,63);(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)(49,55)(50,57)(52,61)(53,54)(56,62)(58,60)(59,63);(48,50)(49,54)(51,57)(52,60)(53,55)(56,63)(58,61)(59,62);(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)(48,49,53,57)(50,59,55,61)(51,56,54,60)(52,62,63,58)Polycyclic presentation:
2^8,47|a^2=h,f^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,g^a=gh,i^a=i^46,d^b=df,e^b=eh,f^b=fh,g^c=gh,i^c=i^46,f^d=fh1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045876);