Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5×S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C23×D5×S4 |
| unambiguous semidirect product | (C5×S4)⋊C24 |
| unambiguous semidirect product | (C5⋊S4)⋊C24 |
| unambiguous semidirect product | (D5×A4)⋊C24 |
| Fitting, socle | C25×C5 ⋊ C2×D3 |
| derived | C5×A4 ⋊ C25 |
| Sylow | C5 ⋊ C24×S4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5×S4 |
| commutator, cosocle, hypocenter | C5×A4 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C25×C5 | C2×D3 |
| LCS | G ▷ C5×A4 | |
| UCS | C1 ◁ C23 | |
10254 conjugacy classes of subgroups; only the 607 normal subgroups are shown.
This group has 10254 conjugacy classes of subgroups — too many to draw. Only its 607 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×A4×S4, C22×D5×GL(2,ℤ/4) |
| maximal normal subgroup of | C2×D5×A4×S4, C22×D5×GL(2,ℤ/4) |
| maximal quotient of | C22×D5×GL(2,ℤ/4), D5×#87493 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240407);