Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#65006 |
| Fitting | C2×C5×#97 ⋊ C2 |
| Sylow | C5 ⋊ C2×#444 |
464 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #12014593, #12014595, #12014600, … |
| maximal normal subgroup of | #12014593, #12014595, #12014600, … |
| maximal quotient of | C2×#10598869, C2×#10598877, C2×#10598870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12318);