Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4⋊C4×Dic10 |
| Sylow | C5 ⋊ Q8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D5 |
| commutator | C22×C5 | C23×C4 |
| Fitting | C4×C5×C4⋊C4 | C2 |
| socle, prime radical, cosocle | C23×C5 | C24 |
| hypercenter | C4×C4⋊C4 | D5 |
| hypocenter | C5 | Q8×C4⋊C4 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #11993473, #11993477, #11993501, … |
| maximal normal subgroup of | #11993473, #11993477, #11993501, … |
| maximal quotient of | C4⋊C4×#683, C4⋊C4×C4⋊Dic5, #95×Dic10, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7449);