Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C17×#432 ⋊ C2 |
| Sylow | C17 ⋊ #1466 |
300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 300 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) = 544 |
Polycyclic presentation:
2^7,17|a^2=e,c^2=fg,e^2=g,b^a=bd,c^a=cg,d^a=df,e^b=ef,h^b=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | #16925944, #16925946, #16925954, … |
| maximal normal subgroup of | #16925944, #16925946, #16925954, … |
| maximal quotient of | #16922510, #16922513, #16922525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2850);