Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D15×D49 |
| unambiguous semidirect product | (C3×D49)⋊(C5×D5) |
| unambiguous semidirect product | (C5×D49)⋊(C5×D3) |
| Fitting, Hall | C3×C52×C49 ⋊ C22 |
| derived | C3×C5×C49 ⋊ C22×C5 |
| Hall | C52×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ C2×C5×D5 |
| Hall | C3×C52 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×C5×D15 |
| Sylow | C52 ⋊ D3×D49 |
| Sylow | C3 ⋊ C5×D5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D15×D49 |
| commutator, cosocle, hypocenter | C3×C5×C49 | C22×C5 |
| Frattini | C7 | C5×D7×D15 |
| Fitting | C3×C52×C49 | C22 |
| socle | C3×C52×C7 | C2×D7 |
| LCS | G ▷ C3×C5×C49 | |
| UCS | C1 ◁ C5 | |
144 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1170 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 158);