Finite Group DatabasebetaFinite Group Databasebeta| order | 6780 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C113 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic3×C113 |
| unambiguous semidirect product | C3⋊(C4×C5×C113) |
| derived, Sylow | C3 ⋊ C4×C5×C113 |
| Hall | C3×C5×C113 ⋊ C4 |
| Hall | C3×C113 ⋊ C4×C5 |
| Hall | C3×C5 ⋊ C4×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C113 | D3 |
| commutator, hypocenter | C3 | C4×C5×C113 |
| Frattini | C2 | C5×D3×C113 |
| Fitting, socle | C2×C3×C5×C113 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C5×C113 | |
24 conjugacy classes of subgroups.
3390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6780, 5);