Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C523 ⋊ C2 |
| Sylow | C523 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4184 |
Polycyclic presentation:
2^5,523|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^522,c^b=ce,f^b=f^5224190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D523, C2×#30660301, #45690220, … |
| maximal normal subgroup of | #104×D523, C2×#30660301, #45690220, … |
| maximal quotient of | #45689934, #45689937, #45689938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 74);