Finite Group DatabasebetaFinite Group Databasebeta| order | 17478 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2913 |
| unambiguous semidirect product | C3⋊(C3×D971) |
| unambiguous semidirect product | C971⋊(C3×D3) |
| Fitting, socle, Hall | C32×C971 ⋊ C2 |
| derived | C3×C971 ⋊ C2×C3 |
| Sylow | C971 ⋊ C3×D3 |
| Sylow | C32 ⋊ D971 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2913 |
| commutator, cosocle, hypocenter | C3×C971 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C971 | C2 |
| LCS | G ▷ C3×C971 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5826 |
4374 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D971, D3×D2913, (C3⋊D3)⋊D971, … |
| maximal normal subgroup of | C3×D3×D971, D3×D2913, (C3⋊D3)⋊D971, … |
| maximal quotient of | C3×Dic2913, C2×C3×D2913 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17478, 8);