Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C89 · Schur multiplier (H2) = C220 |
| direct product | C23×H(5,𝔽2)×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C89 | C24 |
| commutator, Frattini, cosocle | C2 | C27×C89 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C89 ◁ G | |
65726 conjugacy classes of subgroups; only the 58526 normal subgroups are shown.
This group has 65726 conjugacy classes of subgroups — too many to draw. Only its 58526 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5696 |
12104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56086);