Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C271 ⋊ C2 |
| Sylow | C271 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4336 |
Polycyclic presentation:
2^6,271|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^270,d^b=de,e^b=ef,g^b=g^2702716 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46838261, #46838264, #46838311, … |
| maximal normal subgroup of | #46838261, #46838264, #46838311, … |
| maximal quotient of | #46838077, #46838081, #46838152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 987);