Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×C5×D4 ⋊ C22 |
| Hall | C32×C5 ⋊ H(5,𝔽2) |
| Sylow | C32 ⋊ #4144 |
| Sylow | C5 ⋊ #64314 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×(C3⋊D3)⋊D5 |
| commutator, socle, cosocle | C2×C32×C5 | C24 |
| Fitting | C32×C5×D4 | C22 |
| hypercenter | D4 | (C3⋊D3)⋊D5 |
| hypocenter | C32×C5 | H(5,𝔽2) |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^5,3^2,5|d^a=de,f^a=f^2,h^a=h^4,c^b=ce,f^b=f^2,g^b=g^2,d^c=de102 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#64314, #72231751, #72259868 |
| maximal normal subgroup of | D5×#64314, #72231751, #72259868 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5733);