Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#63216 |
| Sylow | C17 ⋊ C2×C22⋊C16 |
272 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #17948638, #17948639, #17948647, … |
| maximal normal subgroup of | #17948638, #17948639, #17948647, … |
| maximal quotient of | C2×#14543704, C2×#14543720, #17958235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20734);