Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C271 ⋊ M64 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^2704360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46834499, #46834500, #46834503, … |
| maximal normal subgroup of | #46834499, #46834500, #46834503, … |
| maximal quotient of | #46834498, C22⋊(C271⋊C32), C4⋊(C271⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 383);