Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C23×C32×C5 ⋊ C22 |
| Hall | C32×C5 ⋊ #120 |
| Sylow | C32 ⋊ #4083 |
| Sylow | C5 ⋊ #63983 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×(C3⋊D3)⋊D5 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C23×C32×C5 | C22 |
| hypercenter | C23 | (C3⋊D3)⋊D5 |
| hypocenter | C32×C5 | #120 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C23 | |
574 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^5,3^2,5|c^a=ce,f^a=f^2,h^a=h^4,c^b=cd,f^b=f^2,g^b=g^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4102);