Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×D4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3300 |
386 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=e,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,d^b=de,f^c=fg,h^c=h^16355 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3300, C2×#14540673, #17910805, … |
| maximal normal subgroup of | D17×#3300, C2×#14540673, #17910805, … |
| maximal quotient of | #17049769, #17050551, #17051479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 16399);