Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | Q8×C4⋊C4×C73 ⋊ C2 |
| Sylow | C73 ⋊ C4×#550 |
3420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=h,b^2=f,c^2=f,d^2=f,e^2=h,b^a=bf,c^a=cg,d^b=df,i^c=i^72,i^e=i^721900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 329420);