Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #123×C257 ⋊ C2 |
| Sylow | C257 ⋊ #458 |
160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4112 |
Polycyclic presentation:
2^6,257|a^2=f,b^a=bd,c^a=ce,e^b=ef,d^c=df,g^c=g^2561808 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45666310, #45666311, #45666316, … |
| maximal normal subgroup of | #45666310, #45666311, #45666316, … |
| maximal quotient of | #45663304, #45663305, #45663309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 738);