Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C89 ⋊ #7213 |
560 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1424 |
Polycyclic presentation:
2^8,89|a^2=d,b^2=e,c^2=fg,b^a=bc,c^a=cf,e^a=efg,f^a=fh,g^a=gh,i^a=i^88,d^b=dg,d^c=dh2504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56593);