Finite Group DatabasebetaFinite Group Databasebeta| order | 10218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×D131⋊C13 |
| unambiguous semidirect product | D131⋊(C3×C13) |
| unambiguous semidirect product | (C3×D131)⋊C13 |
| unambiguous semidirect product | (C131⋊C13)⋊(C2×C3) |
| Fitting, socle, Hall | C3×C131 ⋊ C2×C13 |
| derived, Sylow | C131 ⋊ C2×C3×C13 |
| Hall | C3×C131⋊C13 ⋊ C2 |
| Hall | C131⋊C13 ⋊ C2×C3 |
| Hall | C3×D131 ⋊ C13 |
| Hall | D131 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D131⋊C13 |
| commutator, cosocle, hypocenter | C131 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C131 | C2×C13 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
93 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D131⋊C13, C2×C3×D131⋊C13, C9×D131⋊C13, … |
| maximal normal subgroup of | D3×D131⋊C13, C2×C3×D131⋊C13, C9×D131⋊C13, … |
| maximal quotient of | C3×Dic131⋊C13, C2×C3×D131⋊C13, C9×D131⋊C13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10218, 11);