Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×#344×C89 ⋊ C2 |
| Sylow | C89 ⋊ #21080 |
1000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2848 |
Polycyclic presentation:
2^8,89|a^2=g,b^2=eg,c^2=e,e^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,d^b=dh,i^b=i^88,f^c=fh1994 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 172155);