Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#504 ⋊ C2 |
| Sylow | C17 ⋊ #3415 |
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^7,17|e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^16,e^b=ef,f^b=fg,h^b=h^16,d^c=dg352 conjugacy classes — view the full character table.
| maximal subgroup of | #16955006, #16955010, #16955020, … |
| maximal normal subgroup of | #16955006, #16955010, #16955020, … |
| maximal quotient of | #17187237, #17187368, #17187668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17651);