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 | #157×#170 |
| derived, Hall | C32×C5 ⋊ C4×C8 |
| Sylow | C32 ⋊ C4×#170 |
| Sylow | C5 ⋊ C8×#157 |
| 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×C5×C3⋊D3 | C2×C4 |
| cosocle | C3⋊D3×Dic5 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4659);