Finite Group DatabasebetaFinite Group Databasebeta| order | 19290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C643⋊C3 |
| unambiguous semidirect product | (C2×C643)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×C643)⋊C3 |
| Fitting, socle, Hall | C2×C5×C643 ⋊ C3 |
| derived, Sylow | C643 ⋊ C2×C3×C5 |
| Hall | C5×C643 ⋊ C2×C3 |
| Hall | C2×C643 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C643⋊C3 |
| commutator, cosocle, hypocenter | C643 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C643 | C3 |
| LCS | G ▷ C643 | |
| UCS | C1 ◁ C2×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6430 |
2170 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C5×C643⋊C3, C5×(C643⋊C3)⋊C4, Dic5×C643⋊C3, … |
| maximal normal subgroup of | C4×C5×C643⋊C3, C5×(C643⋊C3)⋊C4, Dic5×C643⋊C3, … |
| maximal quotient of | C4×C5×C643⋊C3, C22×C5×C643⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19290, 2);