Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | Q8×#41×C73 ⋊ C2 |
| Sylow | C73 ⋊ #61316 |
1820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|b^2=f,d^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,g^a=gh,i^a=i^72,c^b=ch,d^b=df,g^c=gh1858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1049384);