Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | #336×C73 ⋊ C4 |
| Sylow | C73 ⋊ C8×#95 |
1174 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=e,b^2=f,c^2=g,e^2=h,g^2=h,b^a=bd,i^c=i^27,i^g=i^72880 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1091830);