Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of C3⋊D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C52×C3⋊D69 |
| unambiguous semidirect product | C3⋊(C52×D69) |
| unambiguous semidirect product | C23⋊(C52×C3⋊D3) |
| Fitting, socle, Hall | C32×C52×C23 ⋊ C2 |
| derived, Hall | C32×C23 ⋊ C2×C52 |
| Hall | C52×C23 ⋊ C3⋊D3 |
| Hall | C32×C52 ⋊ D23 |
| Sylow | C23 ⋊ C52×C3⋊D3 |
| Sylow | C32 ⋊ C52×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C3⋊D69 |
| commutator, cosocle, hypocenter | C32×C23 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C23 | C2 |
| LCS | G ▷ C32×C23 | |
| UCS | C1 ◁ C52 | |
192 conjugacy classes of subgroups.
2625 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D3×D69, C5×D15⋊D69, #35208208, … |
| maximal normal subgroup of | C52×D3×D69, C5×D15⋊D69, #35208208, … |
| maximal quotient of | C52×C3⋊Dic69, C2×C52×C3⋊D69 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 56);