Finite Group DatabasebetaFinite Group Databasebeta| order | 10218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D131⋊C13) |
| unambiguous semidirect product | D393⋊C13 |
| unambiguous semidirect product | (C131⋊C13)⋊D3 |
| Fitting, socle, derived, Hall | C3×C131 ⋊ C2×C13 |
| Hall | C3×C131⋊C13 ⋊ C2 |
| Hall | C131⋊C13 ⋊ D3 |
| Hall | D393 ⋊ C13 |
| Sylow | C131 ⋊ D3×C13 |
| Sylow | C3 ⋊ D131⋊C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C131 | C2×C13 |
| LCS | G ▷ C3×C131 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,131|b^a=b^2,d^a=d^130,d^c=d^10754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10218, 13);