Finite Group DatabasebetaFinite Group Databasebeta| order | 10506 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D103⋊C17) |
| unambiguous semidirect product | D309⋊C17 |
| unambiguous semidirect product | (C103⋊C17)⋊D3 |
| Fitting, socle, derived, Hall | C3×C103 ⋊ C2×C17 |
| Hall | C3×C103⋊C17 ⋊ C2 |
| Hall | C103⋊C17 ⋊ D3 |
| Hall | D309 ⋊ C17 |
| Sylow | C103 ⋊ D3×C17 |
| Sylow | C3 ⋊ D103⋊C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C103 | C2×C17 |
| LCS | G ▷ C3×C103 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,103|b^a=b^2,d^a=d^102,d^c=d^7260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10506, 14);