Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#10587543 |
| Sylow | C17 ⋊ C4×C22⋊C8 |
436 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #17948243, #17948252, #17948258, … |
| maximal normal subgroup of | #17948243, #17948252, #17948258, … |
| maximal quotient of | C8×#10587543, #17951726, #17951736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20234);