Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C257 ⋊ C2 |
| Sylow | C257 ⋊ #360 |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4112 |
Polycyclic presentation:
2^6,257|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^256,c^b=cef,d^b=df,e^b=ef,g^b=g^2562576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #360×D257, C2×#30656548, #45666054, … |
| maximal normal subgroup of | #360×D257, C2×#30656548, #45666054, … |
| maximal quotient of | #45662288, #45662291, #45662330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 360);