Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C271 ⋊ #419 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=e,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^270,c^b=cf,d^b=df2722 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46836336, #46836339, #46836735, … |
| maximal normal subgroup of | #46836336, #46836339, #46836735, … |
| maximal quotient of | #46834759, #46834785, #46834811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 558);