Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10624029 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C22×C22⋊D5 |
| Sylow | C5 ⋊ C2×#3811 |
| 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 | C22×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C22 | |
1078 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#3811, #72231747, C2×#72231393 |
| maximal normal subgroup of | C2×D5×#3811, #72231747 |
| maximal quotient of | #72230430, C2×#72231393 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5322);