Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×D5×Q16 |
| Fitting | C4×C5×Q16 ⋊ C2 |
| Sylow | C5 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1332, #12009051, D5×#1334, … |
| maximal normal subgroup of | D5×#1332, #12009051, D5×#1334, … |
| maximal quotient of | C8×D5×Q16, D5×#1584, D5×#1591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13529);