Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C4 |
| direct product | A4×#4086 |
| unambiguous semidirect product | (C22×#4086)⋊C3 |
| Fitting | C23×C5×D4 ⋊ C2×C3 |
| Hall | C22×#4086 ⋊ C3 |
| Sylow | C5 ⋊ A4×#127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D5×A4 |
| commutator, socle, cosocle | C24×C5 | C23×C3 |
| Fitting | C23×C5×D4 | C2×C3 |
| hypercenter | C2×D4 | D5×A4 |
| hypocenter | C22×C5 | C3×#127 |
| LCS | G ▷ C24×C5 ▷ C22×C5 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
1360 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239883);