Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×#3861 |
| unambiguous semidirect product | C3⋊(C2×C5×#3861) |
| Fitting, socle | C3×C5×C72 ⋊ C2×C3 |
| derived | C3×C72 ⋊ C2×C3×C5 |
| Hall | C3×C5×#3861 ⋊ C2 |
| Hall | C3×#3861 ⋊ C2×C5 |
| Hall | C5×C72 ⋊ C3×D3 |
| Sylow | C72 ⋊ C3×C5×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×#3861 |
| commutator, cosocle, hypocenter | C3×C72 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72 | C2×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C5 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 735 |
285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C25×#3861, C52×D3×#3861, C5×D15×#3861 |
| maximal normal subgroup of | D3×C25×#3861, C52×D3×#3861 |
| maximal quotient of | D3×C25×#3861, C52×D3×#3861, C5×D15×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 102);