Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#711 |
| Fitting | C5×D4×Q8 ⋊ C2 |
| Sylow | C5 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Fitting | C5×D4×Q8 | C2 |
| prime radical | C2×#711 | C22 |
| hypercenter | D4×Q8 | D5 |
| hypocenter | C5 | Q8×#41 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1068 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #12075277, #12075285, #12075292, … |
| maximal normal subgroup of | #12075277, #12075285, #12075292, … |
| maximal quotient of | C4⋊C4×#711, Q8×#4023, Q8×#4038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20726);