Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C73×#2054 ⋊ C2 |
| Sylow | C73 ⋊ #23540 |
1682 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|c^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,c^b=cg,e^b=eh,f^b=fh,g^b=gh,d^c=dh,i^d=i^721204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 197521);