Finite Group DatabasebetaFinite Group Databasebeta| order | 1314 |
| isoclinism | isoclinic class of #10620323 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#10620323 |
| Fitting, socle, Hall | C2×C73 ⋊ C9 |
| derived, Sylow | C73 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10620323 |
| commutator, hypocenter | C73 | C2×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C73 | C9 |
| prime radical | C2×C73⋊C3 | C3 |
| cosocle | C73⋊C3 | C2×C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 146 |
34 conjugacy classes — view the full character table.
| maximal subgroup of | #14581484, C4×#10620323, C2×#10620323⋊C2, … |
| maximal normal subgroup of | #14581484, C4×#10620323, C2×#10620323⋊C2, … |
| maximal quotient of | C4×#10620323, C22×#10620323, D11×#10620323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1314, 8);