Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C73 ⋊ C4 |
| Sylow | C73 ⋊ #62652 |
11674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=h,b^a=bg,f^a=fg,i^a=i^27,e^b=eg,d^c=dg,i^h=i^72742 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116287);