Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C271 ⋊ #350 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^270,c^b=cf,d^b=df2728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D271, C2×#31773681, #46837990, … |
| maximal normal subgroup of | #350×D271, C2×#31773681, #46837990, … |
| maximal quotient of | #46834290, #46834306, D4⋊(C271⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 333);