Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#15692281 |
| Fitting | C22×D4×C101 ⋊ C2 |
| Sylow | C101 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1022 conjugacy classes — view the full character table.
| maximal subgroup of | #27171505, #27171511, #27171609, … |
| maximal normal subgroup of | #27171505, #27171511, #27171609, … |
| maximal quotient of | C2×#20265182, C2×#20265176, C2×#20265217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1336);