Finite Group DatabasebetaFinite Group Databasebeta| order | 7923 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C139 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×C139 |
| unambiguous semidirect product | C19⋊(C3×C139) |
| Fitting, socle, Hall | C19×C139 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C139 | C19⋊C3 |
| commutator, hypocenter | C19 | C3×C139 |
| Frattini | C1 | G |
| Fitting, socle | C19×C139 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C139 | |
8 conjugacy classes of subgroups.
1251 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19⋊C3×C139, C19⋊C3×D139, D19⋊C3×C139, … |
| maximal normal subgroup of | C2×C19⋊C3×C139, C19⋊C3×D139, D19⋊C3×C139, … |
| maximal quotient of | C2×C19⋊C3×C139, C139×#4294, C3×C19⋊C3×C139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7923, 1);