Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #1951 |
196 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^16,d^b=dg,h^b=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | #16951008, #16951009, #16951036, … |
| maximal normal subgroup of | #16951008, #16951009, #16951036, … |
| maximal quotient of | #16932936, #16932946, #16932956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 5291);