Finite Group DatabasebetaFinite Group Databasebeta| order | 19182 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C139⋊C23 |
| unambiguous semidirect product | (C2×C3×C139)⋊C23 |
| Fitting, socle, Hall | C2×C3×C139 ⋊ C23 |
| derived, Sylow | C139 ⋊ C2×C3×C23 |
| Hall | C3×C139 ⋊ C2×C23 |
| Hall | C2×C139 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C139⋊C23 |
| commutator, cosocle, hypocenter | C139 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C139 | C23 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C3 | |
16 conjugacy classes of subgroups.
174 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C139⋊C23, C3×Dic139⋊C23, Dic3×C139⋊C23, … |
| maximal normal subgroup of | C3×C4×C139⋊C23, C3×Dic139⋊C23, Dic3×C139⋊C23, … |
| maximal quotient of | C3×C4×C139⋊C23, C22×C3×C139⋊C23 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19182, 2);