Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C42×Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #34551 |
2082 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=h,d^2=g,e^2=f,b^a=bf,c^a=cg,i^a=i^88,c^b=ch,i^b=i^88,i^c=i^883608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 335885);