Finite Group DatabasebetaFinite Group Databasebeta| order | 16288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C509 ⋊ C4 |
| Sylow | C509 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4072 |
Polycyclic presentation:
2^5,509|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^301,c^b=ce,f^d=f^508649 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#30654279, D509⋊#104, #45656235, … |
| maximal normal subgroup of | C2×#30654279, D509⋊#104, #45656235, … |
| maximal quotient of | D4⋊#16861332, #45656088, #45656089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16288, 210);