Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×C9⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C9⋊(AGL(1,𝔽5)×C41) |
| Fitting, Hall | C5×C9×C41 ⋊ C4 |
| derived, Hall | C5×C9 ⋊ C4×C41 |
| Hall | C9×C41 ⋊ AGL(1,𝔽5) |
| Hall | C5×C41 ⋊ Dic9 |
| Sylow | C9 ⋊ AGL(1,𝔽5)×C41 |
| Sylow | C5 ⋊ Dic9×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C9⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C9 | C4×C41 |
| Frattini | C3 | C41×ΓL(1,𝔽16) |
| Fitting | C5×C9×C41 | C4 |
| socle | C3×C5×C41 | Dic3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C41 | |
36 conjugacy classes of subgroups.
861 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 31);