Finite Group DatabasebetaFinite Group Databasebeta| order | 17578 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D799 |
| unambiguous semidirect product | C17⋊(C11×D47) |
| unambiguous semidirect product | C47⋊(C11×D17) |
| Fitting, socle, Hall | C11×C17×C47 ⋊ C2 |
| derived, Hall | C17×C47 ⋊ C2×C11 |
| Hall | C11×C47 ⋊ D17 |
| Hall | C11×C17 ⋊ D47 |
| Sylow | C47 ⋊ C11×D17 |
| Sylow | C17 ⋊ C11×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D799 |
| commutator, cosocle, hypocenter | C17×C47 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C17×C47 | C2 |
| LCS | G ▷ C17×C47 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8789 |
4411 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D17×D47, D11×D799, D187⋊D47, … |
| maximal normal subgroup of | C11×D17×D47, D11×D799, D187⋊D47, … |
| maximal quotient of | C11×Dic799, C2×C11×D799 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17578, 4);