Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #123×C73 ⋊ C8 |
| Sylow | C73 ⋊ #22357 |
822 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=g,d^2=ef,g^2=h,b^a=be,c^a=cf,d^a=de,i^a=i^63,c^b=ce,i^b=i^10,i^g=i^27,i^h=i^72214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1118194);