Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#11717961 |
| Fitting, derived, Hall | C5×C9×C41 ⋊ C4 |
| Hall | C9×C41 ⋊ AGL(1,𝔽5) |
| Hall | C5×C41 ⋊ Dic9 |
| Hall | C5×C9 ⋊ #4223 |
| Sylow | C41 ⋊ C9⋊AGL(1,𝔽5) |
| Sylow | C9 ⋊ #11717961 |
| Sylow | C5 ⋊ C9⋊#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C41 | C4 |
| Frattini | C3 | C3⋊#11717961 |
| socle | C3×C5×C41 | Dic3 |
| LCS | G ▷ C5×C9×C41 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,41,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^2,e^a=e^32,f^a=f^2,d^b=d^4,e^b=e^40471 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16861480, C9⋊(#11717961⋊C5), C5×C9⋊#11717961, … |
| maximal normal subgroup of | C9⋊(#11717961⋊C5), C5×C9⋊#11717961 |
| maximal quotient of | C9⋊#16861480, C5×C9⋊#11717961, C9⋊#16861518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 32);