Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C271 ⋊ C2 |
| Sylow | C271 ⋊ #388 |
190 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8672 |
Polycyclic presentation:
2^6,271|a^2=f,b^2=df,c^2=d,b^a=bd,c^a=ce,g^b=g^270,g^c=g^2702728 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #388×D271, C2×#31773787, #46838800, … |
| maximal normal subgroup of | #388×D271, C2×#31773787, #46838800, … |
| maximal quotient of | #46834590, #46834596, #46834600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 439);