Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×D4⋊C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #8951 |
636 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=dfg,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,c^b=ch,d^b=dg,e^b=eg,f^b=fg,i^b=i^88,d^c=dg,e^c=eg,f^c=fg2528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 64169);