Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#459 ⋊ C2 |
| Sylow | C17 ⋊ #3253 |
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^16,f^c=fg178 conjugacy classes — view the full character table.
| maximal subgroup of | #17010809, #17010811, #17010842, … |
| maximal normal subgroup of | #17010809, #17010811, #17010842, … |
| maximal quotient of | #17044270, #17044271, #17044724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15889);