Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C17×#433 ⋊ C2 |
| Sylow | C17 ⋊ #3225 |
376 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^16,c^b=ce,d^b=dg,f^c=fg,h^c=h^16250 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3225, C2×#14539895, #17905733, … |
| maximal normal subgroup of | D17×#3225, C2×#14539895, #17905733, … |
| maximal quotient of | #17043711, #17044089, #17044935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15621);