Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#497 ⋊ C2 |
| Sylow | C17 ⋊ #3289 |
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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|a^2=g,b^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=de,e^b=eg,h^b=h^16,f^c=fg,h^c=h^16,e^d=eg,h^d=h^16154 conjugacy classes — view the full character table.
| maximal subgroup of | #16955062, #16955066, #16955076, … |
| maximal normal subgroup of | #16955062, #16955066, #16955076, … |
| maximal quotient of | #17023700, #17023715, #17023745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16285);