Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#64672 |
| Sylow | C5 ⋊ C2×#328 |
336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | #11990178, C4×#64672, #11990188, … |
| maximal normal subgroup of | #11990178, C4×#64672, #11990188, … |
| maximal quotient of | C2×#10597968, C2×#10597971, #11987262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2274);