Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C89 · Schur multiplier (H2) = C27 |
| direct product | C2×C89×#2845 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C89 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C89 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C89 ◁ G | |
1742 conjugacy classes of subgroups; only the 974 normal subgroups are shown.
This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 974 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 22784 |
4628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 29677);