Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C22×C4⋊C4) |
| Fitting | C23×C4×C5 ⋊ C4 |
| Sylow | C5 ⋊ C23×C4⋊C4 |
2488 conjugacy classes of subgroups; only the 1106 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13014611, #13021675, #13021687, … |
| maximal normal subgroup of | #13014611, #13021675, #13021687, … |
| maximal quotient of | C23×(C2×AGL(1,𝔽5))⋊C4, C22×C4×C4⋊AGL(1,𝔽5), C22×#65765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21479);