Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C5 |
| direct product | C3×C37×C3⋊(C5⋊D5) |
| unambiguous semidirect product | C3⋊(C3×C37×C5⋊D5) |
| unambiguous semidirect product | C5⋊(C3×D15×C37) |
| Fitting, socle, Hall | C32×C52×C37 ⋊ C2 |
| derived | C3×C52 ⋊ C2×C3×C37 |
| Hall | C52×C37 ⋊ C3×D3 |
| Hall | C32×C37 ⋊ C5⋊D5 |
| Hall | C32×C52 ⋊ C2×C37 |
| Sylow | C52 ⋊ C3×D3×C37 |
| Sylow | C32 ⋊ C37×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | C3⋊(C5⋊D5) |
| commutator, cosocle, hypocenter | C3×C52 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C3×C37 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5550 |
4329 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D15×C37, C3×D185⋊D15, C3×D37×C3⋊(C5⋊D5), … |
| maximal normal subgroup of | C3×D5×D15×C37, C3×D185⋊D15, C3×D37×C3⋊(C5⋊D5), … |
| maximal quotient of | C3×C37×C3⋊#1039, C2×C3×C37×C3⋊(C5⋊D5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 121);