Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #3166 |
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=eg,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,d^c=dg,h^c=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | #16931945, #16935232, #16935234, … |
| maximal normal subgroup of | #16931945, #16935232, #16935234, … |
| maximal quotient of | #17034760, #17037715, #17038914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15063);