Finite Group DatabasebetaFinite Group Databasebeta| order | 15246 |
| isoclinism | isoclinic class of C3⋊D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C3 |
| direct product | C7×C11×C3⋊D33 |
| unambiguous semidirect product | C3⋊(C7×C11×D33) |
| unambiguous semidirect product | C11⋊(C7×C11×C3⋊D3) |
| Fitting, socle, Hall | C32×C7×C112 ⋊ C2 |
| derived | C32×C11 ⋊ C2×C7×C11 |
| Hall | C32×C112 ⋊ C2×C7 |
| Hall | C7×C112 ⋊ C3⋊D3 |
| Sylow | C112 ⋊ C7×C3⋊D3 |
| Hall | C32×C7 ⋊ C11×D11 |
| Sylow | C32 ⋊ C7×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | C3⋊D33 |
| commutator, cosocle, hypocenter | C32×C11 | C2×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C112 | C2 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C7×C11 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
3927 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×C11×D33, C7×D33⋊D33, C11×D21⋊D33, … |
| maximal normal subgroup of | D3×C7×C11×D33, C7×D33⋊D33, C11×D21⋊D33, … |
| maximal quotient of | C7×C11×C3⋊Dic33, C2×C7×C11×C3⋊D33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15246, 104);