Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3371 |
344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=e,c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^16,f^c=fg253 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3371, C2×#14541548, #17914135, … |
| maximal normal subgroup of | D17×#3371, C2×#14541548, #17914135, … |
| maximal quotient of | #17051006, #17051206, #17053319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 17274);