Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#11763898 |
| Fitting | C2×C8×C17 ⋊ C8 |
| Sylow | C17 ⋊ C2×#334 |
200 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #17981235, #17981237, #17981263, … |
| maximal normal subgroup of | #17981235, #17981237, #17981263, … |
| maximal quotient of | C2×#14545790, C4×#11763898, #17981661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21632);