Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C523 ⋊ C2 |
| Sylow | C523 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^522,d^b=de,f^c=f^5221838 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #137×D523, C2×#30660405, #45691002, … |
| maximal normal subgroup of | #137×D523, C2×#30660405, #45691002, … |
| maximal quotient of | #45690205, #45690212, #45690246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 178);