Finite Group DatabasebetaFinite Group Databasebeta| order | 7350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C3×C5⋊D245 |
| unambiguous semidirect product | C5⋊(C3×D245) |
| Fitting, Hall | C3×C52×C49 ⋊ C2 |
| derived, Hall | C52×C49 ⋊ C2×C3 |
| Hall | C3×C49 ⋊ C5⋊D5 |
| Hall | C3×C52 ⋊ D49 |
| Sylow | C49 ⋊ C3×C5⋊D5 |
| Sylow | C52 ⋊ C3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊D245 |
| commutator, hypocenter | C52×C49 | C2×C3 |
| Frattini | C7 | C3×C5⋊D35 |
| Fitting | C3×C52×C49 | C2 |
| socle | C3×C52×C7 | D7 |
| LCS | G ▷ C52×C49 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
1842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5⋊D5×D49, C3×D5×D245, D3×C5⋊D245, … |
| maximal normal subgroup of | C3×C5⋊D5×D49, C3×D5×D245, D3×C5⋊D245, … |
| maximal quotient of | C3×C49⋊#1039, C2×C3×C5⋊D245, C9×C5⋊D245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7350, 34);