Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic627 |
| unambiguous semidirect product | C11⋊(C3⋊Dic57) |
| unambiguous semidirect product | C19⋊(C3⋊Dic33) |
| derived, Hall | C32×C11×C19 ⋊ C4 |
| Hall | C11×C19 ⋊ C3⋊Dic3 |
| Hall | C32×C19 ⋊ Dic11 |
| Hall | C32×C11 ⋊ Dic19 |
| Sylow | C19 ⋊ C3⋊Dic33 |
| Sylow | C11 ⋊ C3⋊Dic57 |
| Sylow | C32 ⋊ Dic209 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D627 |
| commutator, hypocenter | C32×C11×C19 | C4 |
| Fitting, socle | C2×C32×C11×C19 | C2 |
| LCS | G ▷ C32×C11×C19 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,11,19,2|a^2=f,b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^181884 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 58);