Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×2−1+4×C73 ⋊ C4 |
| Sylow | C73 ⋊ #60070 |
4892 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,e^2=h,b^a=bf,f^a=fh,i^a=i^27,g^b=gh,i^b=i^72,d^c=dh,i^e=i^72,i^g=i^72694 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1114724);