Finite Group DatabasebetaFinite Group Databasebeta| order | 6228 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C173 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3×C173 |
| unambiguous semidirect product | C3⋊(C3×C4×C173) |
| derived | C3 ⋊ C3×C4×C173 |
| Hall | C32×C173 ⋊ C4 |
| Sylow | C32 ⋊ C4×C173 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C173 | D3 |
| commutator, hypocenter | C3 | C3×C4×C173 |
| Frattini | C2 | C3×D3×C173 |
| Fitting, socle | C2×C32×C173 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C3×C173 | |
28 conjugacy classes of subgroups.
3114 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic15×C173, C3×C5×Dic3×C173, C3×ΓL(1,𝔽16)×C173 |
| maximal normal subgroup of | C3×C5×Dic3×C173 |
| maximal quotient of | C3×Dic15×C173, C3×C5×Dic3×C173, C3×ΓL(1,𝔽16)×C173 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6228, 15);