Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C32×C5 ⋊ C4⋊C8 |
| Sylow | C32 ⋊ #3946 |
| Sylow | C5 ⋊ C4⋊AGL(1,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×AGL(1,𝔽9) |
| commutator, Fitting, socle | C2×C32×C5 | C2×C8 |
| prime radical | C2×C5×C3⋊D3 | C2×C4 |
| cosocle | C2×C5×#157 | C22 |
| hypocenter | C32×C5 | C4⋊C8 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^5,3^2,5|a^2=d,b^2=c,c^2=e,b^a=bd,h^a=h^4,f^b=f^2g^2,g^b=f^2,f^c=f^2g,g^c=fg,f^e=f^2,g^e=g^260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4702);