Finite Group DatabasebetaFinite Group Databasebeta| order | 10506 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×D103⋊C17 |
| unambiguous semidirect product | (C3×D103)⋊C17 |
| Fitting, socle, Hall | C3×C103 ⋊ C2×C17 |
| derived, Sylow | C103 ⋊ C2×C3×C17 |
| Hall | C3×C103⋊C17 ⋊ C2 |
| Hall | C103⋊C17 ⋊ C2×C3 |
| Hall | C3×D103 ⋊ C17 |
| Hall | D103 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D103⋊C17 |
| commutator, cosocle, hypocenter | C103 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C103 | C2×C17 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
111 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D103⋊C17, C2×C3×D103⋊C17, C9×D103⋊C17, … |
| maximal normal subgroup of | D3×D103⋊C17, C2×C3×D103⋊C17, C9×D103⋊C17, … |
| maximal quotient of | C3×Dic103⋊C17, C2×C3×D103⋊C17, C9×D103⋊C17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10506, 12);