Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C523 ⋊ C2 |
| Sylow | C523 ⋊ #123 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|c^2=d,b^a=bd,c^a=ce,f^a=f^522,f^c=f^5222624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45690396, #123×D523, C2×#30660357, … |
| maximal normal subgroup of | #45690396, #123×D523, C2×#30660357, … |
| maximal quotient of | #45690066, #45690080, #45690082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 130);