Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C24 |
| direct product | D5×#5948 |
| Fitting | C22×C5×#41 ⋊ C2×C3 |
| Hall | C22×D5×#41 ⋊ C3 |
| Sylow | C5 ⋊ C2×#5948 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D5×C22⋊A4 |
| commutator, cosocle, hypocenter | C22×C5×Q8 | C22×C3 |
| Frattini | C2 | C2×D5×C22⋊A4 |
| Fitting | C22×C5×#41 | C2×C3 |
| socle | C23×C5 | C22×A4 |
| LCS | G ▷ C22×C5×Q8 | |
| UCS | C1 ◁ C4 | |
2310 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 2310 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240379);