Finite Group DatabasebetaFinite Group Databasebeta| order | 19350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C5 |
| direct product | D3×C43×C52⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C43×C52⋊C3) |
| unambiguous semidirect product | (C52×D3)⋊(C3×C43) |
| Fitting, socle | C3×C52×C43 ⋊ C2×C3 |
| derived | C3×C52 ⋊ C2×C3×C43 |
| Hall | C3×C43×C52⋊C3 ⋊ C2 |
| Hall | C52×C43 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ C2×C43 |
| Sylow | C52 ⋊ C3×D3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D3×C52⋊C3 |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C43 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C43 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1935 |
1419 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19350, 93);