Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Hall | C32×C5 ⋊ H(5,𝔽2) |
| Sylow | C32 ⋊ #4144 |
| Sylow | C5 ⋊ #64307 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×D5 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C22×C32×C5 | C23 |
| hypercenter | C22 | D32×D5 |
| hypocenter | C32×C5 | H(5,𝔽2) |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C22 | |
704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|a^2=e,c^a=ce,h^a=h^4,d^b=de,g^b=g^2,f^c=f^299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5326);