Finite Group DatabasebetaFinite Group Databasebeta| order | 19182 |
| isoclinism | isoclinic class of C139⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C2×C23×C139⋊C3 |
| unambiguous semidirect product | (C2×C23×C139)⋊C3 |
| Fitting, socle, Hall | C2×C23×C139 ⋊ C3 |
| derived, Sylow | C139 ⋊ C2×C3×C23 |
| Hall | C23×C139 ⋊ C2×C3 |
| Hall | C2×C139 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | C139⋊C3 |
| commutator, cosocle, hypocenter | C139 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C139 | C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C23 | |
16 conjugacy classes of subgroups.
2254 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C23×C139⋊C3, C23×(C139⋊C3)⋊C4, Dic23×C139⋊C3, … |
| maximal normal subgroup of | C4×C23×C139⋊C3, C23×(C139⋊C3)⋊C4, Dic23×C139⋊C3, … |
| maximal quotient of | C4×C23×C139⋊C3, C22×C23×C139⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19182, 3);