Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C523 ⋊ C22⋊Q8 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^5222624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D523, C2×#30660350, #45690711, … |
| maximal normal subgroup of | C22⋊Q8×D523, C2×#30660350, #45690711, … |
| maximal quotient of | #45690063, #45690077, #45690080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 123);