Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D4×D5×S4 |
| Fitting | C22×C5×D4 ⋊ C2×D3 |
| Sylow | C5 ⋊ C2×D4×S4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Fitting | C22×C5×D4 | C2×D3 |
| socle | C23×C5 | C23×D3 |
| hypercenter | D4 | D5×S4 |
| hypocenter | C5×A4 | C22×D4 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C2 ◁ D4 | |
2590 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×S42, D4×AGL(1,𝔽5)×S4, D5×#11713200, … |
| maximal normal subgroup of | D4×AGL(1,𝔽5)×S4 |
| maximal quotient of | D5×#11713200, #72260259 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240151);