Finite Group DatabasebetaFinite Group Databasebeta| order | 6780 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C113 · Schur multiplier (H2) = C2 |
| direct product | C2×D15×C113 |
| unambiguous semidirect product | (C2×C3)⋊(D5×C113) |
| unambiguous semidirect product | (C2×C5)⋊(D3×C113) |
| Fitting, socle | C2×C3×C5×C113 ⋊ C2 |
| derived, Hall | C3×C5 ⋊ C22×C113 |
| Hall | C3×C5×C113 ⋊ C22 |
| Hall | C5×C113 ⋊ C2×D3 |
| Hall | C3×C113 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×D3×C113 |
| Sylow | C3 ⋊ C2×D5×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C113 | D15 |
| commutator, hypocenter | C3×C5 | C22×C113 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C113 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C113 | |
40 conjugacy classes of subgroups.
2034 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D45×C113, D3×D15×C113, C2×C3×D15×C113, … |
| maximal normal subgroup of | C2×C3×D15×C113, C2×C5×D15×C113 |
| maximal quotient of | C2×D45×C113, D3×D15×C113, C2×C3×D15×C113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6780, 31);