Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C89 · Schur multiplier (H2) = C210 |
| direct product | C89×#36614 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C89 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C89 |
| socle | C23×C89 | C25 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C89 ◁ G | |
7538 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2848 |
7832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 29602);