Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C4×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1916 |
240 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 240 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) = 272 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^8,h^b=h^9,h^f=h^13,h^g=h^1676 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14545931, #17982905, #17982910, … |
| maximal normal subgroup of | C2×#14545931, #17982905, #17982910, … |
| maximal quotient of | #17981738, #17981739, #17981740, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21657);