Finite Group DatabasebetaFinite Group Databasebeta| order | 19038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C167 · Schur multiplier (H2) = C1 |
| direct product | D19⋊C3×C167 |
| unambiguous semidirect product | D19⋊(C3×C167) |
| unambiguous semidirect product | (C19⋊C3)⋊(C2×C167) |
| unambiguous semidirect product | (D19×C167)⋊C3 |
| Fitting, socle, Hall | C19×C167 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C3×C167 |
| Hall | C19⋊C3×C167 ⋊ C2 |
| Hall | D19×C167 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×C167 |
| Hall | D19 ⋊ C3×C167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C167 | D19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C167 |
| Frattini | C1 | G |
| Fitting, socle | C19×C167 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C167 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3173 |
1503 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19⋊C3×D167, C2×D19⋊C3×C167 |
| maximal normal subgroup of | D19⋊C3×D167, C2×D19⋊C3×C167 |
| maximal quotient of | C167×(C19⋊C3)⋊C4, C2×D19⋊C3×C167 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19038, 11);