Finite Group DatabasebetaFinite Group Databasebeta| order | 17574 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D303 |
| unambiguous semidirect product | C3⋊(C29×D101) |
| unambiguous semidirect product | C101⋊(D3×C29) |
| Fitting, socle, Hall | C3×C29×C101 ⋊ C2 |
| derived, Hall | C3×C101 ⋊ C2×C29 |
| Hall | C29×C101 ⋊ D3 |
| Sylow | C101 ⋊ D3×C29 |
| Hall | C3×C29 ⋊ D101 |
| Sylow | C3 ⋊ C29×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D303 |
| commutator, cosocle, hypocenter | C3×C101 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C101 | C2 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8787 |
4437 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C29×D101, D29×D303, D87⋊D101, … |
| maximal normal subgroup of | D3×C29×D101, D29×D303, D87⋊D101, … |
| maximal quotient of | C29×Dic303, C2×C29×D303 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17574, 6);