Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| isoclinism | isoclinic class of C3⋊#1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×C3⋊#1042 |
| unambiguous semidirect product | C3⋊(C49×#1042) |
| Fitting, Hall | C3×C52×C49 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C4×C49 |
| Hall | C52×C49 ⋊ Dic3 |
| Hall | C3×C49 ⋊ #1042 |
| Sylow | C52 ⋊ Dic3×C49 |
| Sylow | C3 ⋊ C49×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | C3⋊#1042 |
| commutator, hypocenter | C3×C52 | C4×C49 |
| Frattini | C7 | C7×C3⋊#1042 |
| Fitting | C3×C52×C49 | C4 |
| socle | C3×C52×C7 | C4×C7 |
| prime radical, cosocle | C3×C5×C7×D5 | C2×C7 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C49 | |
78 conjugacy classes of subgroups.
1617 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 167);