Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C89 · Schur multiplier (H2) = C220 |
| direct product | C2×C89×2−1+6 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | C26 |
| commutator, Frattini, cosocle | C2 | C27×C89 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ G | |
59186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
11570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 56090);