Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#452 ⋊ C2 |
| Sylow | C17 ⋊ #3216 |
390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=g,b^2=e,d^2=g,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 | D17×#3216, C2×#14539792, #17905637, … |
| maximal normal subgroup of | D17×#3216, C2×#14539792, #17905637, … |
| maximal quotient of | #17043667, #17044081, #17044891, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15518);