Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C257 ⋊ C2 |
| Sylow | C257 ⋊ #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) = 8224 |
Polycyclic presentation:
2^6,257|a^2=d,b^2=de,b^a=bd,c^a=ce,c^b=cf,g^c=g^2562582 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45663338, #45663343, #45663365, … |
| maximal normal subgroup of | #45663338, #45663343, #45663365, … |
| maximal quotient of | #45662562, #45662564, #45662583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 484);