Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C17 ⋊ C2 |
| Sylow | C17 ⋊ #3124 |
384 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^16,d^b=dg,h^b=h^16,f^c=fg,h^c=h^16256 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3124, C2×#14539052, #17902690, … |
| maximal normal subgroup of | D17×#3124, C2×#14539052, #17902690, … |
| maximal quotient of | #17034440, #17037406, #17037441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 14778);