Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C24 |
| direct product | #170×C22⋊A4 |
| derived | C24×C5 ⋊ C3×C8 |
| Hall | C24×#170 ⋊ C3 |
| Sylow | C5 ⋊ C8×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×C22⋊A4 |
| commutator, hypocenter | C24×C5 | C3×C8 |
| Fitting, socle | C25×C5 | C3×C4 |
| prime radical | C2×C5×C22⋊A4 | C4 |
| cosocle | C24×Dic5 | C2×C3 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C2 | |
752 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240126);