Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×C3⋊(C7⋊#1044) |
| unambiguous semidirect product | C3⋊(C7×C7⋊#1044) |
| unambiguous semidirect product | C7⋊(C7×C3⋊#1044) |
| Fitting, socle, Hall | C3×C52×C72 ⋊ C4 |
| derived | C3×C52×C7 ⋊ C4×C7 |
| Hall | C52×C72 ⋊ Dic3 |
| Hall | C3×C72 ⋊ #1044 |
| Hall | C3×C52 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ C3⋊#1044 |
| Sylow | C52 ⋊ C7×Dic21 |
| Sylow | C3 ⋊ C7×C7⋊#1044 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(C7⋊#1044) |
| commutator, hypocenter | C3×C52×C7 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C72 | C4 |
| prime radical | C3×C72×C5⋊D5 | C2 |
| cosocle | C3×C7×C5⋊D5 | C2×C7 |
| LCS | G ▷ C3×C52×C7 | |
| UCS | C1 ◁ C7 | |
224 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 224 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.
1050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 699);