Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#518 ⋊ C2 |
| Sylow | C17 ⋊ #1889 |
578 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 93 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=df,b^a=bd,c^a=ce,e^a=eg,h^a=h^16,e^b=eg,d^c=dg,f^c=fg304 conjugacy classes — view the full character table.
| maximal subgroup of | #16950084, #16950086, #16950123, … |
| maximal normal subgroup of | #16950084, #16950086, #16950123, … |
| maximal quotient of | #16929009, #16929019, #16929293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 4918);