Finite Group DatabasebetaFinite Group Databasebeta| order | 11392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #489×C89 ⋊ C2 |
| Sylow | C89 ⋊ #3313 |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,89|a^2=e,b^2=g,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^88,f^c=fg,h^c=h^88,h^d=h^88733 conjugacy classes — view the full character table.
| maximal quotient of | #36570012, #36570760, #36571557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11392, 16575);