Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C17×#485 ⋊ C2 |
| Sylow | C17 ⋊ #3233 |
332 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|b^2=eg,c^2=e,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,h^b=h^16,f^c=fg184 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#3233, C2×#14539966, #17906413, … |
| maximal normal subgroup of | D17×#3233, C2×#14539966, #17906413, … |
| maximal quotient of | #17043830, #17044021, #17044866, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 15692);