Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×#686 |
| Fitting | C2×C4×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | #11993872, #11993873, #11993875, … |
| maximal normal subgroup of | #11993872, #11993873, #11993875, … |
| maximal quotient of | C2×C8×#686, C2×#10601655, C2×#10601634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16102);