Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C73×#1749 ⋊ C2 |
| Sylow | C73 ⋊ #7633 |
640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=e,c^2=h,d^2=g,e^2=h,b^a=bd,c^a=cfh,d^a=df,d^b=dg,e^b=efg,i^b=i^722068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 57817);