Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5×C7 |
| direct product | C52×C3⋊(C7⋊Dic7) |
| unambiguous semidirect product | C3⋊(C52×C7⋊Dic7) |
| unambiguous semidirect product | C7⋊(C52×Dic21) |
| derived, Hall | C3×C72 ⋊ C4×C52 |
| Hall | C3×C52×C72 ⋊ C4 |
| Hall | C52×C72 ⋊ Dic3 |
| Hall | C3×C52 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C52×Dic3 |
| Sylow | C3 ⋊ C52×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | C3⋊(C7⋊D7) |
| commutator, hypocenter | C3×C72 | C4×C52 |
| Frattini | C2 | C52×C3⋊(C7⋊D7) |
| Fitting, socle, prime radical | C2×C3×C52×C72 | C2 |
| cosocle | C2×C3×C72 | C2×C52 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2×C52 | |
480 conjugacy classes of subgroups.
3750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 384);