Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C8×C17 ⋊ C8 |
| Sylow | C17 ⋊ #1564 |
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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=e,b^2=d,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^9,h^e=h^13,h^g=h^1688 conjugacy classes — view the full character table.
| maximal subgroup of | #17981234, #17981236, #17981237, … |
| maximal normal subgroup of | #17981234, #17981236, #17981237, … |
| maximal quotient of | #17981571, C4×#11763898, C4×#11763899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 21634);