Finite Group DatabasebetaFinite Group Databasebeta| order | 19350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×(C5⋊D5)⋊(C43⋊C3) |
| unambiguous semidirect product | (C3×C5⋊D5)⋊(C43⋊C3) |
| Fitting, socle | C3×C52×C43 ⋊ C2×C3 |
| derived, Hall | C52×C43 ⋊ C2×C32 |
| Hall | C3×C52⋊(C43⋊C3) ⋊ C2 |
| Hall | C43×C5⋊D5 ⋊ C32 |
| Hall | C5⋊D5 ⋊ C3×C43⋊C3 |
| Sylow | C43 ⋊ C3×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C2×C3×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C5⋊D5)⋊(C43⋊C3) |
| commutator, cosocle, hypocenter | C52×C43 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C43 | C2×C3 |
| LCS | G ▷ C52×C43 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1935 |
618 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19350, 77);