Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | Dic5×2−1+4 |
| Sylow | C5 ⋊ C4×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator | C2×C5 | C24×C4 |
| Fitting, prime radical | C2×C5×2−1+4 | C2 |
| socle, cosocle | C22×C5 | C25 |
| hypercenter | C2×2−1+4 | D5 |
| hypocenter | C5 | C4×2−1+4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #12105191, Dic5×#454, #12105202, … |
| maximal normal subgroup of | #12105191, Dic5×#454, #12105202, … |
| maximal quotient of | Dic5×#520, Dic5×#519, Dic5×#536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21272);