Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#478 ⋊ C2 |
| Sylow | C17 ⋊ #3251 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|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=fg,h^c=h^16,h^d=h^16178 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3251, C2×#14540145, #17907221, … |
| maximal normal subgroup of | D17×#3251, C2×#14540145, #17907221, … |
| maximal quotient of | #17044251, #17044256, #17044718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15871);