Finite Group DatabasebetaFinite Group Databasebeta| order | 8010 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C89 · Schur multiplier (H2) = C3 |
| direct product | C89×C3⋊D15 |
| unambiguous semidirect product | C3⋊(D15×C89) |
| unambiguous semidirect product | C5⋊(C3⋊D3×C89) |
| Fitting, socle, Hall | C32×C5×C89 ⋊ C2 |
| derived, Hall | C32×C5 ⋊ C2×C89 |
| Hall | C32×C89 ⋊ D5 |
| Hall | C5×C89 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D5×C89 |
| Sylow | C5 ⋊ C3⋊D3×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | C3⋊D15 |
| commutator, hypocenter | C32×C5 | C2×C89 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C89 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C89 | |
48 conjugacy classes of subgroups.
2136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D15×D89, D5×C3⋊D3×C89, D445⋊(C3⋊D3), … |
| maximal normal subgroup of | C3⋊D15×D89, D5×C3⋊D3×C89, D445⋊(C3⋊D3), … |
| maximal quotient of | C89×C3⋊Dic15, C2×C89×C3⋊D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8010, 19);