Finite Group DatabasebetaFinite Group Databasebeta| order | 13806 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C3 |
| direct product | C13×C3⋊D177 |
| unambiguous semidirect product | C3⋊(C13×D177) |
| unambiguous semidirect product | C59⋊(C13×C3⋊D3) |
| Fitting, socle, Hall | C32×C13×C59 ⋊ C2 |
| derived, Hall | C32×C59 ⋊ C2×C13 |
| Hall | C13×C59 ⋊ C3⋊D3 |
| Hall | C32×C13 ⋊ D59 |
| Sylow | C59 ⋊ C13×C3⋊D3 |
| Sylow | C32 ⋊ C13×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C3⋊D177 |
| commutator, cosocle, hypocenter | C32×C59 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C59 | C2 |
| LCS | G ▷ C32×C59 | |
| UCS | C1 ◁ C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6903 |
3471 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C13×D177, D39⋊D177, C13×C3⋊D3×D59, … |
| maximal normal subgroup of | D3×C13×D177, D39⋊D177, C13×C3⋊D3×D59, … |
| maximal quotient of | C13×C3⋊Dic177, C2×C13×C3⋊D177 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13806, 24);