Finite Group DatabasebetaFinite Group Databasebeta| order | 1974 |
| isoclinism | isoclinic class of D329 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D329 |
| unambiguous semidirect product | C47⋊(C3×D7) |
| Fitting, socle, Hall | C3×C7×C47 ⋊ C2 |
| derived, Hall | C7×C47 ⋊ C2×C3 |
| Hall | C3×C47 ⋊ D7 |
| Sylow | C47 ⋊ C3×D7 |
| Hall | C3×C7 ⋊ D47 |
| Sylow | C7 ⋊ C3×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D329 |
| commutator, cosocle, hypocenter | C7×C47 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C47 | C2 |
| LCS | G ▷ C7×C47 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 987 |
498 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D7×D47, D3×D329, D21⋊D47, … |
| maximal normal subgroup of | C3×D7×D47, D3×D329, D21⋊D47, … |
| maximal quotient of | C3×Dic329, C2×C3×D329, C3×D2303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1974, 7);