Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×#126×C73 ⋊ C2 |
| Sylow | C73 ⋊ #34906 |
2062 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|d^2=gh,e^2=f,b^a=bf,c^a=cg,i^a=i^72,c^b=ch,d^b=dh,i^b=i^72,i^c=i^722092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 340993);