Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of D5⋊(C3⋊#157) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D5⋊(C3⋊#157) |
| Fitting, socle, derived, Hall | C33×C5 ⋊ C2×C4 |
| Sylow | C33 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C3⋊#157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C33×C5 | C2×C4 |
| prime radical | C3×D5×C3⋊D3 | C2 |
| cosocle | C3×C3⋊D15 | C22 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
Polycyclic presentation:
2^3,3^3,5|a^2=c,d^a=de,e^a=de^2,f^a=f^2,g^a=g^2,d^b=d^2,e^b=e^2,d^c=d^2,e^c=e^2,g^c=g^442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 512);