Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3333 |
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 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|a^2=eg,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^16,c^b=cg,d^b=de,h^b=h^16,f^c=fg,h^d=h^16253 conjugacy classes — view the full character table.
| maximal subgroup of | #17024061, #17024063, #17024121, … |
| maximal normal subgroup of | #17024061, #17024063, #17024121, … |
| maximal quotient of | #17049989, #17050775, #17051570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16850);