Finite Group DatabasebetaFinite Group Databasebeta| order | 1251 |
| isoclinism | isoclinic class of C139⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C139⋊C3 |
| unambiguous semidirect product | C139⋊C32 |
| unambiguous semidirect product | (C3×C139)⋊C3 |
| Fitting, socle | C3×C139 ⋊ C3 |
| derived, Sylow | C139 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C139⋊C3 |
| commutator, cosocle, hypocenter | C139 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C139 | C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 417 |
147 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D139⋊C3, C3⋊(D139⋊C3), D3×C139⋊C3, … |
| maximal normal subgroup of | C3×D139⋊C3, C3⋊(D139⋊C3), D3×C139⋊C3, … |
| maximal quotient of | C2×C3×C139⋊C3, C9×C139⋊C3, C3×C139⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1251, 3);