Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×D4⋊C8×C89 ⋊ C2 |
| Sylow | C89 ⋊ #10409 |
708 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|c^2=dg,e^2=g,f^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^88,c^b=cf,e^b=eh,f^b=fh,e^c=eg,f^c=fh,i^c=i^882510 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 72934);