Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#11717963 |
| Fitting, Hall | C5×C9×C41 ⋊ C4 |
| derived, Hall | C5×C41 ⋊ C4×C9 |
| Hall | C9×C41 ⋊ AGL(1,𝔽5) |
| Hall | C5×C9 ⋊ Dic41 |
| Sylow | C41 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C9×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #11717963 |
| commutator, hypocenter | C5×C41 | C4×C9 |
| Frattini | C3 | C3×#11717963 |
| Fitting | C5×C9×C41 | C4 |
| socle | C3×C5×C41 | C3×C4 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
765 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#16861482, C9×#11717963⋊C5, C5×C9×#11717963, … |
| maximal normal subgroup of | C9×#11717963⋊C5, C5×C9×#11717963 |
| maximal quotient of | C9×#16861482, C5×C9×#11717963, C9×#16861520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 26);