Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C4⋊C8×C73 ⋊ C2 |
| Sylow | C73 ⋊ #29435 |
724 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=fh,b^2=e,c^2=h,d^2=gh,f^2=h,b^a=be,c^a=cf,d^a=de,c^b=cg,f^c=fh,i^c=i^722938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 272686);