Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C49 · Schur multiplier (H2) = C5 |
| direct product | C52×D3×C49 |
| unambiguous semidirect product | C3⋊(C2×C52×C49) |
| Fitting, Hall | C3×C52×C49 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C52×C49 |
| Hall | C3×C49 ⋊ C2×C52 |
| Hall | C3×C52 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C49 | D3 |
| commutator, hypocenter | C3 | C2×C52×C49 |
| Frattini | C7 | C52×D3×C7 |
| Fitting | C3×C52×C49 | C2 |
| socle | C3×C52×C7 | C2×C7 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C52×C49 | |
96 conjugacy classes of subgroups.
3675 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D3×D49, C5×D3×D5×C49, C5×D3×D245, … |
| maximal normal subgroup of | C52×D3×D49, C5×D3×D5×C49, C5×D3×D245, … |
| maximal quotient of | C52×Dic3×C49, C2×C52×D3×C49, C52×D9×C49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 35);