Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| derived, Hall | C32×C5 ⋊ C4×C8 |
| Sylow | C32 ⋊ C8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C8×#157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D5⋊#157 |
| commutator, hypocenter | C32×C5 | C4×C8 |
| Fitting | C32×C4×C5 | C2×C4 |
| socle | C2×C32×C5 | C42 |
| prime radical | C2×C3⋊D15 | C2×C4 |
| cosocle | C4×C3⋊D15 | C22 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C4 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,b^2=d,c^2=e,d^2=e,f^a=fg,g^a=fg^2,h^a=h^2,f^b=f^2,g^b=g^2,f^c=f^2,g^c=g^2,h^c=h^472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1846);