Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#15692320 |
| Fitting | C2×Q8×C101 ⋊ C4 |
| Sylow | C101 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
278 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#15692320, #27186896, #27186909, … |
| maximal normal subgroup of | C4×#15692320, #27186896, #27186909, … |
| maximal quotient of | C2×#20266025, C2×Q8⋊#11717581, #27186426, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1545);