Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×ΓL(1,𝔽16) |
| 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 ⋊ D3×C3⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C2×C16 |
| Fitting | C32×C4×C5 | C2×C4 |
| socle | C2×C32×C5 | C2×C8 |
| prime radical | C2×C3×D15 | C8 |
| cosocle | C32×#168 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
122 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,b^2=d,c^2=d,d^2=e,f^a=f^2,h^a=h^2,g^b=g^2,h^c=h^4108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1776);