Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D7×C25×D21 |
| unambiguous semidirect product | (C3×D7)⋊(D7×C25) |
| unambiguous semidirect product | (C7×D7)⋊(D3×C25) |
| Fitting, Hall | C3×C72×C25 ⋊ C22 |
| derived, Hall | C3×C72 ⋊ C22×C25 |
| Hall | C72×C25 ⋊ C2×D3 |
| Hall | C3×C25 ⋊ D72 |
| Sylow | C72 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ D72×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D7×D21 |
| commutator, hypocenter | C3×C72 | C22×C25 |
| Frattini | C5 | C5×D7×D21 |
| Fitting | C3×C72×C25 | C22 |
| socle, cosocle | C3×C5×C72 | C22×C5 |
| prime radical | C5×D7×D21 | C5 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C25 | |
156 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 156 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.
1500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 270);