Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×Q8×D5 |
| Fitting | C2×C4×C5×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C22×C4×Q8 |
1664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #11990669, D5×#1461, D5×#1467, … |
| maximal normal subgroup of | #11990669, D5×#1461, D5×#1467, … |
| maximal quotient of | C2×C4×D5×C4⋊C4, C42×Q8×D5, C2×C4×#4033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19788);