Finite Group DatabasebetaFinite Group Databasebeta| order | 10410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D347 |
| unambiguous semidirect product | C347⋊(C2×C3×C5) |
| Fitting, socle, Hall | C3×C5×C347 ⋊ C2 |
| derived, Sylow | C347 ⋊ C2×C3×C5 |
| Hall | C5×C347 ⋊ C2×C3 |
| Hall | C3×C347 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D347 |
| commutator, cosocle, hypocenter | C347 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C347 | C2 |
| LCS | G ▷ C347 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
2625 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D347, C5×D3×D347, D15×D347, … |
| maximal normal subgroup of | C3×D5×D347, C5×D3×D347, D15×D347, … |
| maximal quotient of | C3×C5×Dic347, C2×C3×C5×D347, C5×C9×D347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10410, 2);