Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×C32 |
| Fitting | C2×C5×C32 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D5 |
| commutator, hypocenter | C5 | C22×C32 |
| Frattini | C16 | C22×D5 |
| Fitting | C2×C5×C32 | C2 |
| socle | C22×C5 | C2×C16 |
| prime radical | C22×D5 | C16 |
| cosocle | C5×C16 | C23 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | #11987108, C4×D5×C32, D5×#1397, … |
| maximal normal subgroup of | #11987108, C4×D5×C32, D5×#1397, … |
| maximal quotient of | C4×D5×C32, C2×Dic5×C32, D5×C22⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2239);