Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊(C5⋊(#120⋊C3)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C3⋊(C5⋊(#120⋊C3)) |
| unambiguous semidirect product | C5⋊(C3⋊(#120⋊C3)) |
| unambiguous semidirect product | #91842⋊C3 |
| Fitting, derived | C24×C3×C5 ⋊ C2×C3 |
| Sylow | C5 ⋊ C3⋊(#120⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C24×C3×C5 | C2×C3 |
| Frattini | C22 | A4×D15 |
| socle | C22×C3×C5 | C2×A4 |
| LCS | G ▷ C24×C3×C5 | |
| UCS | C1 | |
154 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 19 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:
2,3,2^4,3,5|c^a=ce,d^a=def,g^a=g^2,h^a=h^4,c^b=cd,d^b=c,e^b=f,f^b=ef66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2557);