Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×#87938 |
| unambiguous semidirect product | D101⋊(C4×D4) |
| Fitting | C2×D4×C101 ⋊ C4 |
| Sylow | C101 ⋊ C2×C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×#87938 |
| commutator | C2×C101 | C23×C4 |
| Frattini | C2 | C23×#87938 |
| Fitting | C2×D4×C101 | C4 |
| socle | C22×C101 | C22×C4 |
| hypercenter | C2×D4 | #87938 |
| hypocenter | C101 | C2×C4×D4 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
290 conjugacy classes — view the full character table.
| maximal subgroup of | #99×#87938, #100×#87938, #102×#87938, … |
| maximal normal subgroup of | #99×#87938, #100×#87938, #102×#87938, … |
| maximal quotient of | C2×C22⋊C4×#87938, C2×C4⋊C4×#87938, C4×D4×#87938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1613);