Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×#126×C89 ⋊ C2 |
| Sylow | C89 ⋊ #34849 |
2160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
Polycyclic presentation:
2^8,89|b^2=g,c^2=gh,e^2=f,b^a=bf,c^a=cg,i^a=i^88,c^b=ch,d^b=dh,i^c=i^88,i^d=i^882540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 340068);