Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×Q8⋊#3633 |
| Fitting | C2×Q8×C17 ⋊ C8 |
| Sylow | C17 ⋊ C2×Q8⋊C8 |
280 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 280 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 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Q8⋊#3633, #17981612, #103×#3633, … |
| maximal normal subgroup of | C4×Q8⋊#3633, #17981612, #103×#3633, … |
| maximal quotient of | C2×#14545784, C2×#14545785, #17981513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21627);