Finite Group DatabasebetaFinite Group Databasebeta| order | 16206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#22549194 |
| Fitting, socle, Hall | C2×C37×C73 ⋊ C3 |
| derived, Hall | C37×C73 ⋊ C2×C3 |
| Hall | C2×C73 ⋊ C37⋊C3 |
| Hall | C2×C37 ⋊ C73⋊C3 |
| Sylow | C73 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ C2×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22549194 |
| commutator, cosocle, hypocenter | C37×C73 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C73 | C3 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5402 |
1806 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22549194, #44569412, #44569416, … |
| maximal normal subgroup of | C4×#22549194, #44569412, #44569416, … |
| maximal quotient of | C4×#22549194, C22×#22549194 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16206, 4);