Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#63241 |
| Sylow | C17 ⋊ D4⋊C16 |
110 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=d,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^9,c^b=ce,h^d=h^13,h^f=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D4⋊#63241, #17982037, #17982039, … |
| maximal normal subgroup of | C2×D4⋊#63241, #17982037, #17982039, … |
| maximal quotient of | #17981121, #17981123, #17981125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21552);