Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×C37⋊#3874 |
| Fitting, socle | C3×C52×C37 ⋊ D3 |
| derived | C37×C52⋊C3 ⋊ C2×C3 |
| Hall | C3×C37×C52⋊C3 ⋊ C2 |
| Hall | C52×C37 ⋊ C3×D3 |
| Hall | C3×C52⋊C3 ⋊ D37 |
| Sylow | C37 ⋊ C3×#3874 |
| Sylow | C52 ⋊ C3×D111 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C37⋊#3874 |
| commutator, cosocle, hypocenter | C37×C52⋊C3 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | D3 |
| LCS | G ▷ C37×C52⋊C3 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1665 |
633 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D37×#3874, C3×#3874⋊D37, C3×((C5⋊D5)⋊C3)⋊D37, … |
| maximal normal subgroup of | C3×D37×#3874, C3×#3874⋊D37, C3×((C5⋊D5)⋊C3)⋊D37, … |
| maximal quotient of | C3×#26012787, C2×C3×C37⋊#3874 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 88);