Finite Group DatabasebetaFinite Group Databasebeta| order | 6976 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16812626 |
| Sylow | C109 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 71 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 | C4×#16812626, #104×Dic109, #28362842, … |
| maximal normal subgroup of | C4×#16812626, #104×Dic109, #28362842, … |
| maximal quotient of | C2×D4⋊#11724784, C2×Q8⋊#11724784, #28361414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6976, 562);