Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5×C7 |
| direct product | C52×C22⋊#3862 |
| unambiguous semidirect product | C22⋊(C52×#3862) |
| unambiguous semidirect product | (C22×C5)⋊(C5×#3862) |
| Fitting, socle, Hall | C22×C52×C72 ⋊ C3 |
| derived, Hall | C22×C72 ⋊ C3×C52 |
| Hall | C52×C72 ⋊ A4 |
| Hall | C22×C52 ⋊ #3862 |
| Sylow | C72 ⋊ C52×A4 |
| Sylow | C22 ⋊ C52×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C22⋊#3862 |
| commutator, cosocle, hypocenter | C22×C72 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52×C72 | C3 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C52 | |
240 conjugacy classes of subgroups.
1700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 742);