Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ #127 |
| Sylow | C32 ⋊ #4086 |
| Sylow | C5 ⋊ #64149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C3⋊D15 |
| commutator, socle, cosocle | C22×C32×C5 | C23 |
| Fitting | C2×C32×C5×D4 | C2 |
| hypercenter | C2×D4 | C3⋊D15 |
| hypocenter | C32×C5 | #127 |
| LCS | G ▷ C22×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
648 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3^2,5|a^2=e,b^a=be,c^a=ce,f^a=f^2,g^a=g^2,h^a=h^4,c^b=cd234 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#64149, C3⋊D3×#4086, #127×C3⋊D15 |
| maximal normal subgroup of | D5×#64149, C3⋊D3×#4086, #127×C3⋊D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4519);