Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C257 ⋊ C2 |
| Sylow | C257 ⋊ #453 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2056 |
Polycyclic presentation:
2^6,257|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^256,d^b=df,e^b=ef,d^c=df2192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45666302, #45666314, #45666324, … |
| maximal normal subgroup of | #45666302, #45666314, #45666324, … |
| maximal quotient of | #45663238, #45663243, #45663266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 717);