Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C73 ⋊ C8 |
| Sylow | C73 ⋊ #23336 |
728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=e,d^2=e,g^2=h,b^a=be,c^a=cf,d^a=def,i^a=i^10,c^b=cef,d^b=de,i^g=i^27,i^h=i^72202 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1118237);