Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | D4×C4⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #34127 |
2698 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=h,c^2=f,e^2=fg,b^a=bf,c^a=cg,d^b=df,i^c=i^88,i^e=i^882300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 329025);