Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7 |
| direct product | C5×D3×C5⋊(C7⋊D7) |
| unambiguous semidirect product | (C5×D3)⋊(C5×C7⋊D7) |
| unambiguous semidirect product | (D3×C7)⋊(C5×D35) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C22 |
| derived | C3×C5×C72 ⋊ C22×C5 |
| Hall | C52×C72 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×C5×D5 |
| Hall | C3×C52 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C5×D3×D5 |
| Sylow | C52 ⋊ D3×C7⋊D7 |
| Sylow | C3 ⋊ C2×C5×C5⋊(C7⋊D7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3×C5⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C3×C5×C72 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C22 |
| LCS | G ▷ C3×C5×C72 | |
| UCS | C1 ◁ C5 | |
480 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 689);