Finite Group DatabasebetaFinite Group Databasebeta| order | 13818 |
| isoclinism | isoclinic class of D147 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D147 |
| unambiguous semidirect product | C3⋊(C47×D49) |
| unambiguous semidirect product | C49⋊(D3×C47) |
| Fitting, Hall | C3×C47×C49 ⋊ C2 |
| derived, Hall | C3×C49 ⋊ C2×C47 |
| Hall | C47×C49 ⋊ D3 |
| Hall | C3×C47 ⋊ D49 |
| Sylow | C49 ⋊ D3×C47 |
| Sylow | C3 ⋊ C47×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D147 |
| commutator, cosocle, hypocenter | C3×C49 | C2×C47 |
| Frattini | C7 | D21×C47 |
| Fitting | C3×C47×C49 | C2 |
| socle | C3×C7×C47 | D7 |
| LCS | G ▷ C3×C49 | |
| UCS | C1 ◁ C47 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6909 |
3525 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D147, D3×C47×D49, D141⋊D49, … |
| maximal normal subgroup of | D47×D147, D3×C47×D49, D141⋊D49, … |
| maximal quotient of | C47×Dic147, C2×C47×D147 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13818, 11);