Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C89 · Schur multiplier (H2) = C211 |
| direct product | C22×B(4,𝔽2)×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C89 | #120 |
| commutator, Frattini, cosocle | C23 | C25×C89 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C25×C89 ◁ G | |
7014 conjugacy classes of subgroups; only the 1134 normal subgroups are shown.
This group has 7014 conjugacy classes of subgroups — too many to draw. Only its 1134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2848 |
5696 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 53380);