Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of A4×(C24⋊C5)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23 |
| direct product | A4×(C24⋊C5)⋊C2 |
| Fitting, socle | C26 ⋊ C3×D5 |
| derived | C22×C24⋊C5 ⋊ C2×C3 |
| Hall | C22×(C24⋊C5)⋊C2 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C24⋊C5 | C2×C3 |
| Fitting, socle | C26 | C3×D5 |
| LCS | G ▷ C22×C24⋊C5 | |
| UCS | C1 | |
536 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 30 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#11757162, A5×(C24⋊C5)⋊C2, A4×#11757163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240394);