Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#15692285 |
| Sylow | C101 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 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 | #27171499, #27171501, #27171603, … |
| maximal normal subgroup of | #27171499, #27171501, #27171603, … |
| maximal quotient of | C2×#20265185, C2×#20265178, C2×#20265220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1341);