Finite Group DatabasebetaFinite Group Databasebeta| order | 10509 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C113 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×C113 |
| unambiguous semidirect product | C31⋊(C3×C113) |
| unambiguous semidirect product | (C31×C113)⋊C3 |
| Fitting, socle, Hall | C31×C113 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C3×C113 |
| Frattini | C1 | G |
| Fitting, socle | C31×C113 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C113 | |
8 conjugacy classes of subgroups.
1469 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C31⋊C3×C113, C31⋊C3×D113, C113×D31⋊C3, … |
| maximal normal subgroup of | C2×C31⋊C3×C113, C31⋊C3×D113, C113×D31⋊C3, … |
| maximal quotient of | C2×C31⋊C3×C113, C113×C31⋊C9, C3×C31⋊C3×C113 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10509, 1);