Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C17×#347 ⋊ C2 |
| Sylow | C17 ⋊ #2180 |
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|a^2=e,c^2=ef,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^16,d^b=dfg,e^b=eg,f^b=fg,h^b=h^16,d^c=dg199 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#2180, C2×#14530677, #17187771, … |
| maximal normal subgroup of | D17×#2180, C2×#14530677, #17187771, … |
| maximal quotient of | #16946199, #16946205, #16946277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 6403);