Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of (C24⋊C5)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×(C24⋊C5)⋊C2 |
| Fitting | C24×C4 ⋊ D5 |
| derived | C24⋊C5 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | (C24⋊C5)⋊C2 |
| commutator, hypocenter | C24⋊C5 | C2×C4 |
| Frattini | C2 | C2×(C24⋊C5)⋊C2 |
| Fitting | C24×C4 | D5 |
| socle | C25 | C2×D5 |
| prime radical | C2×(C24⋊C5)⋊C2 | C2 |
| cosocle | C2×C24⋊C5 | C22 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C4 | |
358 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20 |
40 conjugacy classes — view the full character table.
| maximal subgroup of | ((C24⋊C5)⋊C2)⋊C8, #13046101, C4×#66297, … |
| maximal normal subgroup of | ((C24⋊C5)⋊C2)⋊C8, #13046101, C4×#66297, … |
| maximal quotient of | C4×#66245, #13046118, #13046119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21458);