Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #3374 |
326 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 326 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) = 2176 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,c^b=cg,d^b=de,h^b=h^16,f^c=fg181 conjugacy classes — view the full character table.
| maximal subgroup of | #17024305, #17024307, #17024365, … |
| maximal normal subgroup of | #17024305, #17024307, #17024365, … |
| maximal quotient of | #17050975, #17051181, #17053306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17317);