Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×#3874 |
| unambiguous semidirect product | (C37×#3874)⋊C3 |
| Fitting, socle, Hall | C52×C37 ⋊ C3×D3 |
| derived | C37×C52⋊C3 ⋊ C2×C3 |
| Hall | C52⋊C3×C37⋊C3 ⋊ C2 |
| Sylow | C37 ⋊ C3×#3874 |
| Sylow | C52 ⋊ D3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C37×C52⋊C3 | C2×C3 |
| Fitting, socle | C52×C37 | C3×D3 |
| LCS | G ▷ C37×C52⋊C3 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 555 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | #3874×D37⋊C3, #3874⋊(D37⋊C3), C37⋊C3×#3874⋊C2, … |
| maximal normal subgroup of | #3874×D37⋊C3, #3874⋊(D37⋊C3), C37⋊C3×#3874⋊C2, … |
| maximal quotient of | C37⋊C3×#64470, C2×C37⋊C3×#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 72);