Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C523 ⋊ #103 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16736 |
Polycyclic presentation:
2^5,523|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^5222624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #103×D523, C2×#30660296, #45690198, … |
| maximal normal subgroup of | #103×D523, C2×#30660296, #45690198, … |
| maximal quotient of | #45689935, #45689941, #45689950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 69);