Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#10624043 |
| Hall | C32×C5 ⋊ C2×#41 |
| Sylow | C32 ⋊ C2×#711 |
| Sylow | C5 ⋊ C2×#3804 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D32×D5 |
| commutator, cosocle | C2×C32×C5 | C24 |
| Frattini | C2 | C2×D32×D5 |
| Fitting, socle | C22×C32×C5 | C23 |
| hypocenter | C32×C5 | C2×#41 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
710 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5343);