Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×C8×C22⋊D5 |
| Fitting | C23×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C2×C8×D4 |
616 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#3938, #11989847, #11992191, … |
| maximal normal subgroup of | C8×#3938, #11989847, #11992191, … |
| maximal quotient of | C2×C8×#686, C2×C8×#687, C2×C8×#688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17545);