Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C271 ⋊ C2 |
| Sylow | C271 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^2704360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16864637, #46834643, #46834646, … |
| maximal normal subgroup of | C8×#16864637, #46834643, #46834646, … |
| maximal quotient of | #46836109, C4×(C2×D271)⋊C8, C4×Dic271⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 600);