Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×H(5,𝔽2)×C73 ⋊ C4 |
| Sylow | C73 ⋊ #33359 |
1356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=f,e^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^27,e^b=eh,f^b=fgh,d^c=dh,f^e=fh,i^f=i^72658 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1113531);