Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #346×C73 ⋊ C4 |
| Sylow | C73 ⋊ C4×#365 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,c^2=de,d^2=g,e^2=gh,g^2=h,b^a=bd,f^a=fh,d^b=dg,e^b=egh,g^b=gh,i^b=i^27,i^c=i^72,i^f=i^72784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1096295);