Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C3×C4 |
| direct product | AGL(1,𝔽5)×#622 |
| derived, Hall | C32×C5 ⋊ C4×C8 |
| Sylow | C32 ⋊ C8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#622 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×#157 |
| commutator, hypocenter | C32×C5 | C4×C8 |
| Fitting, socle | C2×C32×C5 | C42 |
| prime radical | C2×C32×D5 | C2×C4 |
| cosocle | D5×C3⋊Dic3 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
148 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4658);