Finite Group DatabasebetaFinite Group Databasebeta| order | 4302 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C239 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C239 |
| unambiguous semidirect product | C3⋊(C2×C3×C239) |
| Fitting, socle, Hall | C32×C239 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C239 |
| Sylow | C32 ⋊ C2×C239 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C239 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C3×C239 |
| Frattini | C1 | G |
| Fitting, socle | C32×C239 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C239 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 245 |
| transitive degree | μt(G) = 1434 |
2151 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D3×C239, C3×D15×C239, C3×D3×C239⋊C7, … |
| maximal normal subgroup of | C3×C5×D3×C239, C3×D3×C239⋊C7, C3×D3×C7×C239 |
| maximal quotient of | C3×C5×D3×C239, C3×D15×C239, C3⋊AGL(1,𝔽7)×C239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4302, 7);