Finite Group DatabasebetaFinite Group Databasebeta| order | 17344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C271 ⋊ C2 |
| Sylow | C271 ⋊ #399 |
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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=d,b^2=de,b^a=bd,c^a=ce,c^b=cf,g^c=g^2702722 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46835382, #46835387, #46835409, … |
| maximal normal subgroup of | #46835382, #46835387, #46835409, … |
| maximal quotient of | #46834606, #46834608, #46834627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 484);