Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#441 ⋊ C2 |
| Sylow | C17 ⋊ C4×#137 |
484 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^c=h^16,h^d=h^16220 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#137×D17, C2×#14537600, #17898407, … |
| maximal normal subgroup of | C4×#137×D17, C2×#14537600, #17898407, … |
| maximal quotient of | #17003746, #17003915, #17003941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 13326);