Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #117×C73 ⋊ C8 |
| Sylow | C73 ⋊ #20543 |
1090 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=f,b^2=g,c^2=e,f^2=h,g^2=h,b^a=be,d^a=de,i^a=i^22,c^b=ce,i^b=i^10,i^f=i^46,i^g=i^27,i^h=i^72316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1118133);