Finite Group DatabasebetaFinite Group Databasebeta| order | 16641 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1849⋊C9 |
| derived, Sylow | C1849 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C1849⋊C3 |
| commutator, hypocenter | C1849 | C9 |
| Frattini, socle, prime radical | C3×C43 | C43⋊C3 |
| Fitting, cosocle | C3×C1849 | C3 |
| LCS | G ▷ C1849 | |
| UCS | C1 ◁ C3 | |
9 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16641 |
Polycyclic presentation:
3,43,3,43|a^3=c,b^43=d^24,b^a=b^36d,d^a=d^361857 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D1849⋊C9, C2×C1849⋊C9 |
| maximal normal subgroup of | D1849⋊C9, C2×C1849⋊C9 |
| maximal quotient of | C2×C1849⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16641, 2);