Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×#121×C73 ⋊ C4 |
| Sylow | C73 ⋊ D4×#99 |
2102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=g,b^a=be,c^a=cf,f^a=fh,i^a=i^27,d^b=de,i^b=i^72,g^c=gh,i^d=i^72,i^g=i^72559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1109677);