Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C17×C22⋊C16 ⋊ C2 |
| Sylow | C17 ⋊ #1314 |
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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=d,d^2=f,f^2=g,b^a=bc,c^a=ce,d^b=de,h^b=h^16364 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1314, C2×#14526707, #16943384, … |
| maximal normal subgroup of | D17×#1314, C2×#14526707, #16943384, … |
| maximal quotient of | #16920942, #16920944, #16920946, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2433);