Finite Group DatabasebetaFinite Group Databasebeta| order | 19182 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D139⋊C3 |
| unambiguous semidirect product | (C23×D139)⋊C3 |
| Fitting, socle, Hall | C23×C139 ⋊ C2×C3 |
| derived, Sylow | C139 ⋊ C2×C3×C23 |
| Hall | C23×C139⋊C3 ⋊ C2 |
| Hall | C23×D139 ⋊ C3 |
| Hall | C139⋊C3 ⋊ C2×C23 |
| Hall | D139 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D139⋊C3 |
| commutator, cosocle, hypocenter | C139 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C139 | C2×C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
667 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D139⋊C3, C2×C23×D139⋊C3 |
| maximal normal subgroup of | D23×D139⋊C3, C2×C23×D139⋊C3 |
| maximal quotient of | C23×(C139⋊C3)⋊C4, C2×C23×D139⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19182, 15);