Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C271 ⋊ #474 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=d,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^270,e^c=ef1909 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #474×D271, C2×#31774175, #46846148, … |
| maximal normal subgroup of | #474×D271, C2×#31774175, #46846148, … |
| maximal quotient of | #46836362, #46836609, #46836613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 827);