Finite Group DatabasebetaFinite Group Databasebeta| order | 19158 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D309 |
| unambiguous semidirect product | C3⋊(C31×D103) |
| unambiguous semidirect product | C103⋊(D3×C31) |
| Fitting, socle, Hall | C3×C31×C103 ⋊ C2 |
| derived, Hall | C3×C103 ⋊ C2×C31 |
| Hall | C31×C103 ⋊ D3 |
| Sylow | C103 ⋊ D3×C31 |
| Hall | C3×C31 ⋊ D103 |
| Sylow | C3 ⋊ C31×D103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D309 |
| commutator, cosocle, hypocenter | C3×C103 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C103 | C2 |
| LCS | G ▷ C3×C103 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9579 |
4836 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C31×D103, D31×D309, D93⋊D103, … |
| maximal normal subgroup of | D3×C31×D103, D31×D309, D93⋊D103, … |
| maximal quotient of | C31×Dic309, C2×C31×D309 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19158, 10);