Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×Q8×C271 ⋊ C2 |
| Sylow | C271 ⋊ #460 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^270,e^c=ef2719 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46835423, #46835425, #46835429, … |
| maximal normal subgroup of | #46835423, #46835425, #46835429, … |
| maximal quotient of | #46835712, #46835724, #46835734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 749);