Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C523 ⋊ C2 |
| Sylow | C523 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4184 |
Polycyclic presentation:
2^5,523|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^522,d^b=de,f^b=f^5222621 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45690374, #45690375, #45690379, … |
| maximal normal subgroup of | #45690374, #45690375, #45690379, … |
| maximal quotient of | #45690207, #45690211, #45690247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 174);