Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×C22⋊Q8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #34691 |
2464 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^b=i^88,i^c=i^882540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 337627);