Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C271 ⋊ C2 |
| Sylow | C271 ⋊ #476 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=df,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^270,e^c=ef,g^c=g^2702719 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46835481, #46835482, #46835492, … |
| maximal normal subgroup of | #46835481, #46835482, #46835492, … |
| maximal quotient of | #46836365, #46836628, #46836950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 840);