Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(#4223⋊C5)) |
| unambiguous semidirect product | (C3⋊(C3⋊#4223))⋊C5 |
| Fitting, socle, derived, Hall | C32×C41 ⋊ C4×C5 |
| Hall | C32×C41⋊C5 ⋊ C4 |
| Hall | C3⋊(C3⋊#4223) ⋊ C5 |
| Hall | C41⋊C5 ⋊ C3⋊Dic3 |
| Sylow | C41 ⋊ C5×C3⋊Dic3 |
| Sylow | C32 ⋊ #4223⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C41 | C4×C5 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,3^2,41|a^2=c,d^a=d^2,e^a=e^2,f^a=f^32,f^b=f^10,f^c=f^4078 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 71);