Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C257 ⋊ C2 |
| Sylow | C257 ⋊ #394 |
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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|c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^256,g^c=g^2562582 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #394×D257, C2×#30656653, #45667532, … |
| maximal normal subgroup of | #394×D257, C2×#30656653, #45667532, … |
| maximal quotient of | #45662559, #45662565, #45662566, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 465);