Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#11756747 |
| Sylow | C5 ⋊ C2×#5919 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D5×S4 |
| commutator, cosocle | C2×C5×A4 | C24 |
| Frattini | C2 | C22×D5×S4 |
| Fitting | C23×C4×C5 | C2×D3 |
| socle | C24×C5 | C22×D3 |
| hypercenter | C2×C4 | D5×S4 |
| hypocenter | C5×A4 | C2×#41 |
| LCS | G ▷ C2×C5×A4 ▷ C5×A4 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
1690 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1690 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
130 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240130);