Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | Dic5×#95 |
| Sylow | C5 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C22×D5 |
| commutator | C2×C5 | C43 |
| Fitting | C2×C5×#95 | C2 |
| socle, prime radical, cosocle | C24×C5 | C23 |
| hypercenter | C2×#95 | D5 |
| hypocenter | C5 | C4×#95 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
752 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 325 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #11990173, Dic5×#327, #11990178, … |
| maximal normal subgroup of | #11990173, Dic5×#327, #11990178, … |
| maximal quotient of | #11987219, Dic5×#336, #12004448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2275);