Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C23×D4×C73 ⋊ C4 |
| Sylow | C73 ⋊ #20598 |
5982 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=g,e^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^27,e^b=eh,i^g=i^72784 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1104441);