Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| isoclinism | isoclinic class of C41⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C4×C41⋊C5 |
| unambiguous semidirect product | (C4×C41)⋊(C32×C5) |
| unambiguous semidirect product | (C3×C4×C41)⋊(C3×C5) |
| unambiguous semidirect product | (C32×C4×C41)⋊C5 |
| Fitting, Hall | C32×C4×C41 ⋊ C5 |
| derived, Sylow | C41 ⋊ C32×C4×C5 |
| Hall | C32×C41 ⋊ C4×C5 |
| Hall | C4×C41 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C4 | C41⋊C5 |
| commutator, hypocenter | C41 | C32×C4×C5 |
| Frattini | C2 | C2×C32×C41⋊C5 |
| Fitting | C32×C4×C41 | C5 |
| socle | C2×C32×C41 | C2×C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C32×C4 | |
72 conjugacy classes of subgroups.
468 conjugacy classes — view the full character table.
| maximal subgroup of | C32×Dic5×C41⋊C5, C32×C4×C5×C41⋊C5, C32×AGL(1,𝔽5)×C41⋊C5 |
| maximal normal subgroup of | C32×C4×C5×C41⋊C5 |
| maximal quotient of | C32×C4×C41⋊C25, C32×Dic5×C41⋊C5, C32×C4×C5×C41⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 55);