Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D8×C523 ⋊ C2 |
| Sylow | C523 ⋊ D16 |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^5221838 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D16×D523, C2×#30660314, #45690635, … |
| maximal normal subgroup of | D16×D523, C2×#30660314, #45690635, … |
| maximal quotient of | #45690005, #45690006, #45690030, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 87);