Finite Group DatabasebetaFinite Group Databasebeta| order | 6228 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#10621924 |
| unambiguous semidirect product | C3⋊(C3×#10621924) |
| Fitting, socle, Hall | C32×C173 ⋊ C4 |
| derived | C3×C173 ⋊ C3×C4 |
| Sylow | C173 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ #10621924 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#10621924 |
| commutator, hypocenter | C3×C173 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C173 | C4 |
| LCS | G ▷ C3×C173 | |
| UCS | C1 ◁ C3 | |
28 conjugacy classes of subgroups.
405 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×C3⋊#10621924, C3×C3⋊#16812337, C3×C3⋊#16812338, … |
| maximal normal subgroup of | C3×C5×C3⋊#10621924 |
| maximal quotient of | C3×C5×C3⋊#10621924, C3×C3⋊#16812337, C3×C3⋊#16812338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6228, 21);