Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| isoclinism | isoclinic class of C3⋊D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C3 |
| direct product | C19×C3⋊Dic33 |
| unambiguous semidirect product | C3⋊(C19×Dic33) |
| unambiguous semidirect product | C11⋊(C19×C3⋊Dic3) |
| derived, Hall | C32×C11 ⋊ C4×C19 |
| Hall | C32×C11×C19 ⋊ C4 |
| Hall | C11×C19 ⋊ C3⋊Dic3 |
| Hall | C32×C19 ⋊ Dic11 |
| Sylow | C11 ⋊ C19×C3⋊Dic3 |
| Sylow | C32 ⋊ C19×Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | C3⋊D33 |
| commutator, hypocenter | C32×C11 | C4×C19 |
| Frattini | C2 | C19×C3⋊D33 |
| Fitting, socle | C2×C32×C11×C19 | C2 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C2×C19 | |
72 conjugacy classes of subgroups.
1938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 57);