Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | Q8×C4⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #34374 |
2098 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=h,b^2=g,c^2=g,d^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,i^c=i^88,i^d=i^882276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 332477);