Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C73×#2345 ⋊ C2 |
| Sylow | C73 ⋊ #22535 |
1172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=eh,c^2=e,d^2=e,b^a=be,c^a=cf,f^a=fh,d^b=de,g^c=gh,i^c=i^721855 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 186319);