Finite Group DatabasebetaFinite Group Databasebeta| order | 10470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D349⋊C3 |
| unambiguous semidirect product | D349⋊(C3×C5) |
| unambiguous semidirect product | (C349⋊C3)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D349)⋊C3 |
| Fitting, socle, Hall | C5×C349 ⋊ C2×C3 |
| derived, Sylow | C349 ⋊ C2×C3×C5 |
| Hall | C5×C349⋊C3 ⋊ C2 |
| Hall | C5×D349 ⋊ C3 |
| Hall | C349⋊C3 ⋊ C2×C5 |
| Hall | D349 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D349⋊C3 |
| commutator, cosocle, hypocenter | C349 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C349 | C2×C3 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
320 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#13063703⋊C3, #20296124⋊C3, D5×D349⋊C3, … |
| maximal normal subgroup of | C5×#13063703⋊C3, #20296124⋊C3, D5×D349⋊C3, … |
| maximal quotient of | C5×Dic349⋊C3, C2×C5×D349⋊C3, C5×D349⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10470, 10);