Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(#4294⋊C4) |
| unambiguous semidirect product | #4294⋊Dic11 |
| derived, Hall | C11×C19 ⋊ C4×C9 |
| Hall | C11×#4294 ⋊ C4 |
| Hall | Dic209 ⋊ C9 |
| Hall | #4294 ⋊ Dic11 |
| Sylow | C19 ⋊ C9×Dic11 |
| Sylow | C11 ⋊ #4294⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C11⋊(D19⋊C3) |
| commutator, hypocenter | C11×C19 | C4×C9 |
| Fitting, socle | C2×C3×C11×C19 | C2×C3 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,19,2,3|a^2=e,b^3=f,c^a=c^10,d^a=d^18,d^b=d^11324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 4);