Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊(C5⋊#1020) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23×C3 |
| unambiguous semidirect product | C3⋊(C5⋊#1020) |
| unambiguous semidirect product | C5⋊(C3⋊#1020) |
| Fitting, socle | C24×C3×C5 ⋊ D3 |
| derived | C3×C5×C22⋊A4 ⋊ C2 |
| Sylow | C5 ⋊ C3⋊#1020 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×C22⋊A4 | C2 |
| Fitting, socle | C24×C3×C5 | D3 |
| LCS | G ▷ C3×C5×C22⋊A4 | |
| UCS | C1 | |
268 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2,3^2,5,2^4|b^a=b^2,c^a=c^2,d^a=d^4,e^a=ef,g^a=gh,e^b=f,f^b=ef,g^b=h,h^b=gh66 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C3⋊#1020, D15×#1020, D3×C5⋊#1020, … |
| maximal normal subgroup of | D5×C3⋊#1020, D15×#1020, D3×C5⋊#1020, … |
| maximal quotient of | #72230913, C3×C3⋊(C5⋊#1020), #72277882 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5932);