Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4×C4⋊C4×C73 ⋊ C2 |
| Sylow | C73 ⋊ #17546 |
1194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2336 |
Polycyclic presentation:
2^8,73|a^2=f,c^2=g,d^2=gh,e^2=h,b^a=be,c^a=cg,e^a=eg,e^b=eh,f^b=fgh,i^b=i^722944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 136756);