Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#4094⋊C3) |
| unambiguous semidirect product | #91837⋊C3 |
| Sylow | C5 ⋊ C3⋊(#131⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | A4×D15 |
| commutator, hypocenter | C3×C5×Q8 | C3×C4 |
| Fitting, cosocle | C3×C5×#41 | C2×C3 |
| socle | C2×C3×C5 | C4×A4 |
| prime radical | C3×C5×#41⋊C3 | C2 |
| LCS | G ▷ C3×C5×Q8 | |
| UCS | C1 ◁ C4 | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2,3,2^3,3,5,2|a^2=c,c^2=h,d^2=h,e^2=h,f^a=f^2,g^a=g^4,d^b=de,e^b=d,e^d=eh126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2556);