Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic41⋊C5) |
| unambiguous semidirect product | Dic369⋊C5 |
| derived, Hall | C9×C41 ⋊ C4×C5 |
| Hall | C9×C41⋊C5 ⋊ C4 |
| Hall | Dic369 ⋊ C5 |
| Hall | C41⋊C5 ⋊ Dic9 |
| Sylow | C41 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ Dic41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C9⋊(D41⋊C5) |
| commutator, hypocenter | C9×C41 | C4×C5 |
| Frattini | C2×C3 | C3⋊(D41⋊C5) |
| Fitting | C2×C9×C41 | C2×C5 |
| socle | C2×C3×C41 | C5×D3 |
| LCS | G ▷ C9×C41 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,41,2,3|a^2=e,c^3=f^2,c^a=c^2f,d^a=d^40,f^a=f^2,d^b=d^37132 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9⋊(Dic41⋊C5), C9⋊(Dic205⋊C5), C9⋊(#11717963⋊C5) |
| maximal normal subgroup of | C5×C9⋊(Dic41⋊C5) |
| maximal quotient of | C9⋊(Dic41⋊C25), C5×C9⋊(Dic41⋊C5), C9⋊(Dic205⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 4);