Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| isoclinism | isoclinic class of D111 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×D111 |
| unambiguous semidirect product | C3⋊(C3×C52×D37) |
| Fitting, socle, Hall | C32×C52×C37 ⋊ C2 |
| derived | C3×C37 ⋊ C2×C3×C52 |
| Hall | C52×C37 ⋊ C3×D3 |
| Hall | C32×C37 ⋊ C2×C52 |
| Hall | C32×C52 ⋊ D37 |
| Sylow | C37 ⋊ C3×C52×D3 |
| Sylow | C32 ⋊ C52×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | D111 |
| commutator, cosocle, hypocenter | C3×C37 | C2×C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C2 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C3×C52 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5550 |
4275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C52×D3×D37, C3×C5×D5×D111, C3×C5×D15⋊D37, … |
| maximal normal subgroup of | C3×C52×D3×D37, C3×C5×D5×D111, C3×C5×D15⋊D37, … |
| maximal quotient of | C3×C52×Dic111, C2×C3×C52×D111 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 124);