Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C25 |
| direct product | C23×C24⋊C5 |
| unambiguous semidirect product | C27⋊C5 |
| Fitting, socle, Sylow | C27 ⋊ C5 |
| derived | C24 ⋊ C23×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C24⋊C5 |
| commutator, cosocle, hypocenter | C24 | C23×C5 |
| Frattini | C1 | G |
| Fitting, socle | C27 | C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C23 | |
5900 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×C24⋊C5, C22×C4×C24⋊C5, C2×D4×C24⋊C5, … |
| maximal normal subgroup of | C22⋊C4×C24⋊C5, C22×C4×C24⋊C5, C2×D4×C24⋊C5, … |
| maximal quotient of | C22×C4×C24⋊C5, C2×D4×C24⋊C5, C2×Q8×C24⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21538);