Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C17×#585 ⋊ C2 |
| Sylow | C17 ⋊ #3027 |
772 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 161 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|d^2=g,b^a=be,c^a=cf,d^a=dg,h^a=h^16,f^b=fg,e^c=eg301 conjugacy classes — view the full character table.
| maximal subgroup of | #16953306, #16953309, #16953311, … |
| maximal normal subgroup of | #16953306, #16953309, #16953311, … |
| maximal quotient of | #17008295, #17008302, #17008309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13912);