Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C89×#3416 ⋊ C2 |
| Sylow | C89 ⋊ #33855 |
640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=h,b^2=h,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^88,d^b=de,e^b=eg,g^b=gh,f^c=fh,e^d=eg,g^d=gh1445 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 326329);