Finite Group DatabasebetaFinite Group Databasebeta| order | 7524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#4296⋊C4 |
| unambiguous semidirect product | #4296⋊(C4×C11) |
| derived, Sylow | C19 ⋊ C4×C9×C11 |
| Hall | C11×#4296 ⋊ C4 |
| Hall | C11×Dic19 ⋊ C9 |
| Hall | C11×C19 ⋊ C4×C9 |
| Hall | #4296 ⋊ C4×C11 |
| Hall | Dic19 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C4×C9×C11 |
| Frattini | C2 | C11×AGL(1,𝔽19) |
| Fitting, socle | C2×C11×C19 | C2×C9 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C11 | |
36 conjugacy classes of subgroups.
418 conjugacy classes — view the full character table.
| maximal subgroup of | C11⋊C5×#4296⋊C4, C5×C11×#4296⋊C4, C11×#4296⋊Dic5, … |
| maximal normal subgroup of | C11⋊C5×#4296⋊C4, C5×C11×#4296⋊C4 |
| maximal quotient of | C5×C11×#4296⋊C4, C11×#4296⋊Dic5, C11×#4296⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7524, 36);