Finite Group DatabasebetaFinite Group Databasebeta| order | 16208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D1013⋊C8 |
| derived, Sylow | C1013 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16860990 |
| commutator, hypocenter | C1013 | C2×C8 |
| Frattini | C2 | C2×#16860990 |
| Fitting | C4×C1013 | C4 |
| socle | C2×C1013 | C2×C4 |
| prime radical | C2×D1013 | C4 |
| cosocle | Dic1013 | C22 |
| LCS | G ▷ C1013 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8104 |
Polycyclic presentation:
2^4,1013|a^2=c,c^2=d,e^a=e^968,e^b=e^1012,e^c=e^10121028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16860990, #44569706, #44569714, … |
| maximal normal subgroup of | C8×#16860990, #44569706, #44569714, … |
| maximal quotient of | C4×#22549208, #44569709, #44569719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16208, 48);