Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
| unambiguous semidirect product | C4⋊(C3⋊(C3⋊D15)) |
| Fitting | C33×C4×C5 ⋊ C2 |
| Hall | C33×C5 ⋊ D4 |
| Sylow | C33 ⋊ D20 |
| Sylow | C5 ⋊ C4⋊(C3⋊(C3⋊D3)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C3⋊(C3⋊D15) |
| commutator, socle, cosocle | C2×C33×C5 | C22 |
| Fitting | C33×C4×C5 | C2 |
| hypercenter | C4 | C3⋊(C3⋊D15) |
| hypocenter | C33×C5 | D4 |
| LCS | G ▷ C2×C33×C5 ▷ C33×C5 | |
| UCS | C1 ◁ C2 ◁ C4 | |
448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
Polycyclic presentation:
2^3,3^3,5|b^2=c,b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^4273 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 481);