Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×#672 |
| derived, Sylow | C5 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D5 |
| commutator, hypocenter | C5 | C23×C16 |
| Frattini | C8 | C23×D5 |
| Fitting | C23×C5×C8 | C2 |
| socle, prime radical | C24×C5 | C8 |
| cosocle | C5×C8 | C24 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C8 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598295, C2×#10598148, #12014143, … |
| maximal normal subgroup of | C2×#10598295, C2×#10598148, #12014143, … |
| maximal quotient of | C22×C4×#672, C22×C22⋊#672, C22×C4⋊#672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17535);