Finite Group DatabasebetaFinite Group Databasebeta| order | 7923 |
| isoclinism | isoclinic class of C139⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C139⋊C3 |
| unambiguous semidirect product | C139⋊(C3×C19) |
| Fitting, socle, Hall | C19×C139 ⋊ C3 |
| derived, Sylow | C139 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C139⋊C3 |
| commutator, hypocenter | C139 | C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C139 | C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
931 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19×C139⋊C3, C19×D139⋊C3, D19×C139⋊C3, … |
| maximal normal subgroup of | C2×C19×C139⋊C3, C19×D139⋊C3, D19×C139⋊C3, … |
| maximal quotient of | C2×C19×C139⋊C3, C19×C139⋊C9, C3×C19×C139⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7923, 2);