Finite Group DatabasebetaFinite Group Databasebeta| order | 714 |
| isoclinism | isoclinic class of D119 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D119 |
| unambiguous semidirect product | C17⋊(C3×D7) |
| Fitting, socle, Hall | C3×C7×C17 ⋊ C2 |
| derived, Hall | C7×C17 ⋊ C2×C3 |
| Hall | C3×C17 ⋊ D7 |
| Hall | C3×C7 ⋊ D17 |
| Sylow | C17 ⋊ C3×D7 |
| Sylow | C7 ⋊ C3×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D119 |
| commutator, cosocle, hypocenter | C7×C17 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C17 | C2 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 357 |
183 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D7×D17, D3×D119, D21⋊D17, … |
| maximal normal subgroup of | C3×D7×D17, D3×D119, D21⋊D17, … |
| maximal quotient of | C3×Dic119, C2×C3×D119, C9×D119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(714, 7);