Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | D5×D15×C49 |
| unambiguous semidirect product | (C3×D5)⋊(D5×C49) |
| unambiguous semidirect product | (C5×D5)⋊(D3×C49) |
| Fitting, Hall | C3×C52×C49 ⋊ C22 |
| derived, Hall | C3×C52 ⋊ C22×C49 |
| Hall | C52×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ D52 |
| Sylow | C52 ⋊ C2×D3×C49 |
| Sylow | C3 ⋊ D52×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D5×D15 |
| commutator, hypocenter | C3×C52 | C22×C49 |
| Frattini | C7 | C7×D5×D15 |
| Fitting | C3×C52×C49 | C22 |
| socle, cosocle | C3×C52×C7 | C22×C7 |
| prime radical | C7×D5×D15 | C7 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C49 | |
144 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1764 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 174);