Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16812625 |
| Fitting | C2×M16×C109 ⋊ C2 |
| Sylow | C109 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28362836, C4×#16812625, #28362841, … |
| maximal normal subgroup of | #28362836, C4×#16812625, #28362841, … |
| maximal quotient of | C2×#20294753, C2×#20294756, #28361412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 561);