Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16812731 |
| Fitting | C2×Q16×C109 ⋊ C2 |
| Sylow | C109 ⋊ C2×#137 |
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
778 conjugacy classes — view the full character table.
| maximal subgroup of | #28371848, C4×#16812731, #28371870, … |
| maximal normal subgroup of | #28371848, C4×#16812731, #28371870, … |
| maximal quotient of | C2×#20295033, C2×#20295026, C2×#20295067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 1343);