Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#435×C89 ⋊ C2 |
| Sylow | C89 ⋊ #21492 |
1058 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=g,b^2=e,d^2=g,g^2=h,b^a=be,c^a=cf,c^b=ch,i^b=i^88,d^c=dh2540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 175677);