Finite Group DatabasebetaFinite Group Databasebeta| order | 10731 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×C49⋊C3 |
| unambiguous semidirect product | C49⋊(C3×C73) |
| Fitting, Hall | C49×C73 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C3×C73 |
| Frattini | C7 | ΓL(1,𝔽8)×C73 |
| Fitting | C49×C73 | C3 |
| socle | C7×C73 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C73 | |
12 conjugacy classes of subgroups.
1387 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C73×C49⋊C3, D73×C49⋊C3, C73×D49⋊C3, … |
| maximal normal subgroup of | C2×C73×C49⋊C3, D73×C49⋊C3, C73×D49⋊C3, … |
| maximal quotient of | C2×C73×C49⋊C3, C73×C49⋊C9, C3×C73×C49⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10731, 2);