Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#491 ⋊ C2 |
| Sylow | C17 ⋊ #3135 |
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 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) = 1088 |
Polycyclic presentation:
2^7,17|b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^16,c^b=cg,h^c=h^16,h^d=h^16160 conjugacy classes — view the full character table.
| maximal subgroup of | #16945501, #16954682, #17015523, … |
| maximal normal subgroup of | #16945501, #16954682, #17015523, … |
| maximal quotient of | #17034523, #17036958, #17037982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14857);