Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×D5×GL(2,ℤ/4) |
| Fitting | C25×C5 ⋊ C2×D3 |
| Sylow | C5 ⋊ C22×GL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D5×S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Frattini | C2 | C22×D5×S4 |
| Fitting | C25×C5 | C2×D3 |
| socle | C24×C5 | C22×D3 |
| hypercenter | C23 | D5×S4 |
| hypocenter | C5×A4 | C22×D4 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C22 ◁ C23 | |
3222 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 3222 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×A4⋊S4, C2×AGL(1,𝔽5)×GL(2,ℤ/4), C22×D5×GL(2,ℤ/4) |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×GL(2,ℤ/4), C22×D5×GL(2,ℤ/4) |
| maximal quotient of | C2×D5×#5429, C22×D5×GL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240230);