Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C89 ⋊ #14665 |
1530 conjugacy classes of subgroups; only the 411 normal subgroups are shown.
This group has 1530 conjugacy classes of subgroups — too many to draw. Only its 411 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=h,d^2=ef,b^a=be,c^a=cf,c^b=cg,d^b=def,i^b=i^88,d^c=de2516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 100624);