Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C32×C5 ⋊ C4×D4 |
| Sylow | C32 ⋊ D4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #63879 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D32×AGL(1,𝔽5) |
| commutator, Fitting, socle | C2×C32×C5 | C22×C4 |
| prime radical | D5×#625 | C2 |
| cosocle | C2×C32×D5 | C23 |
| hypocenter | C32×C5 | C4×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
402 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 76 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:
2^5,3^2,5|a^2=d,c^a=ce,h^a=h^2,c^b=ce,f^b=f^2,g^c=g^2,h^d=h^469 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×#67, D3×#67⋊AGL(1,𝔽5), #72230057, … |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#67, D3×#67⋊AGL(1,𝔽5), #72230057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4730);