Finite Group DatabasebetaFinite Group Databasebeta| order | 6228 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#10621924 |
| Fitting, socle, Hall | C32×C173 ⋊ C4 |
| derived, Sylow | C173 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #10621924 |
| commutator, hypocenter | C173 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C173 | C4 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C32 | |
36 conjugacy classes of subgroups.
423 conjugacy classes — view the full character table.
| maximal subgroup of | C32×C5×#10621924, C32×#16812337, C32×#16812338, … |
| maximal normal subgroup of | C32×C5×#10621924 |
| maximal quotient of | C32×C5×#10621924, C32×#16812337, C32×#16812338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6228, 20);