Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C89 · Schur multiplier (H2) = C210 |
| direct product | C23×#100×C89 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C89 | C22⋊C4 |
| commutator | C22 | C24×C4×C89 |
| Frattini, cosocle | C2×C4 | C25×C89 |
| prime radical | C24×D4×C89 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C89 ◁ C24×C4×C89 ◁ G | |
7134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5696 |
7832 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 53059);