Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C82×C17 ⋊ C2 |
| Sylow | C17 ⋊ #1335 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^7,17|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^16,c^b=ce,e^b=eg,h^b=h^16556 conjugacy classes — view the full character table.
| maximal subgroup of | D17×#1335, C2×#14526758, #16944109, … |
| maximal normal subgroup of | D17×#1335, C2×#14526758, #16944109, … |
| maximal quotient of | #16920974, #16920977, #16920992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2484);