Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#10587550 |
| Fitting | C4×Q8×C17 ⋊ C4 |
| Sylow | C17 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#10587550, #17951935, #17951939, … |
| maximal normal subgroup of | C8×#10587550, #17951935, #17951939, … |
| maximal quotient of | C4×#11763657, C4×Q8⋊#3624, #17951867, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20271);