Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | D4×#63241 |
| Sylow | C17 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | D8×#63241, #17982275, #17982277, … |
| maximal normal subgroup of | D8×#63241, #17982275, #17982277, … |
| maximal quotient of | D8×#63241, SD16×#63241, Q16×#63241, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21717);