Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C4×C22⋊C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #22401 |
1908 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|a^2=g,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^88,d^b=deh,i^b=i^88,i^d=i^883596 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 184865);