Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C271 ⋊ C2 |
| Sylow | C271 ⋊ #486 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^270,g^b=g^270,g^c=g^2701912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46835453, #46835454, #46835460, … |
| maximal normal subgroup of | #46835453, #46835454, #46835460, … |
| maximal quotient of | #46836491, #46837046, #46837169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 897);