Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D525 |
| unambiguous semidirect product | (C2×C3)⋊(C7×D175) |
| unambiguous semidirect product | (C2×C7)⋊(C7×D75) |
| unambiguous semidirect product | (C2×C25)⋊(C7×D21) |
| Fitting | C2×C3×C72×C25 ⋊ C2 |
| derived | C3×C7×C25 ⋊ C22×C7 |
| Hall | C3×C72×C25 ⋊ C22 |
| Hall | C72×C25 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D25 |
| Hall | C3×C25 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ C2×D75 |
| Sylow | C25 ⋊ C2×C7×D21 |
| Sylow | C3 ⋊ C2×C7×D175 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D525 |
| commutator, cosocle, hypocenter | C3×C7×C25 | C22×C7 |
| Frattini | C5 | C2×C7×D105 |
| Fitting | C2×C3×C72×C25 | C2 |
| socle | C2×C3×C5×C72 | D5 |
| LCS | G ▷ C3×C7×C25 | |
| UCS | C1 ◁ C2×C7 | |
156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3696 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 308);