Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#4088 |
| Fitting | C2×C4×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #11993914, #11993920, #11993928, … |
| maximal normal subgroup of | #11993914, #11993920, #11993928, … |
| maximal quotient of | C8×#4088, #12068894, #12068914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16240);