Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×#997 |
| Fitting, derived | C5×H(5,𝔽2) ⋊ C3×C4 |
| Hall | AGL(1,𝔽5)×H(5,𝔽2) ⋊ C3 |
| Sylow | C5 ⋊ C4×#997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×C22⋊A4 |
| commutator, Fitting, hypocenter | C5×H(5,𝔽2) | C3×C4 |
| socle | C2×C5 | C4×C22⋊A4 |
| prime radical | D5×#997 | C2 |
| cosocle | D5×H(5,𝔽2) | C2×C3 |
| LCS | G ▷ C5×H(5,𝔽2) | |
| UCS | C1 ◁ C2 | |
690 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
55 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240125);