Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ D16 |
| Sylow | C32 ⋊ #3958 |
| Sylow | C5 ⋊ #63653 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10623757 |
| commutator, Fitting, cosocle | C32×C5×C8 | C22 |
| Frattini, hypercenter | C8 | D5×C3⋊D3 |
| socle | C2×C32×C5 | D8 |
| hypocenter | C32×C5 | D16 |
| LCS | G ▷ C32×C5×C8 ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3^2,5|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,h^a=h^4,c^b=cd,d^b=de,f^b=f^2,g^b=g^2117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1022);