Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C3×C82×D5 |
| Fitting | C3×C5×C82 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C3×C82 |
| Hall | C3×C5 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C82 | D5 |
| commutator, hypocenter | C5 | C2×C3×C82 |
| Frattini | C42 | C22×C3×D5 |
| Fitting | C3×C5×C82 | C2 |
| socle | C22×C3×C5 | C2×C42 |
| prime radical | C22×C3×D5 | C42 |
| cosocle | C42×C5 | C23×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C82 | |
560 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 354 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 6002);