Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,c^2=e,e^2=f,f^2=g,b^a=bd,h^a=h^8,h^c=h^9,h^e=h^13,h^f=h^16100 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545992, D4×#10587665, #17983137, … |
| maximal normal subgroup of | C2×#14545992, D4×#10587665, #17983137, … |
| maximal quotient of | #17982275, #17982297, #17982298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21718);