Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5×#4625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| direct product | D5×#4625 |
| derived | C5×C22⋊A4 ⋊ C2×C4 |
| Sylow | C5 ⋊ C2×#4625 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C5×C22⋊A4 | C2×C4 |
| Frattini | C23 | D5×S4 |
| Fitting | C5×#120 | C2×D3 |
| socle | C22×C5 | C2×SL(2,ℤ/4) |
| prime radical | D5×#120⋊C3 | C2 |
| cosocle | C5×#120⋊C3 | C22 |
| LCS | G ▷ C5×C22⋊A4 | |
| UCS | C1 | |
282 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
44 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#11714270, AGL(1,𝔽5)×#4625, D5×#4625⋊C2, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#4625, D5×#4625⋊C2, #72243737 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237408);