Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C32×C5 ⋊ C2×C16 |
| Sylow | C32 ⋊ D5×C16 |
| Sylow | C5 ⋊ #63542 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D3×D15 |
| commutator, hypocenter | C32×C5 | C2×C16 |
| Fitting, cosocle | C32×C5×C8 | C22 |
| socle | C2×C32×C5 | C2×C8 |
| prime radical | C2×C3⋊D15 | C8 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C8 | |
134 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,b^2=c,c^2=d,d^2=e,f^a=f^2,h^a=h^4,g^b=g^2216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1126);