Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C89×#1273 ⋊ C2 |
| Sylow | C89 ⋊ #8147 |
618 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 199 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=e,b^2=f,c^2=e,e^2=g,f^2=h,b^a=bd,c^a=cg,c^b=ch,i^b=i^88,i^c=i^883608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 60052);