Finite Group DatabasebetaFinite Group Databasebeta| order | 15804 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C439⋊C9) |
| unambiguous semidirect product | C439⋊(C22⋊C9) |
| derived, Hall | C22×C439 ⋊ C9 |
| Sylow | C439 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ C439⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C439⋊C3) |
| commutator, hypocenter | C22×C439 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C439 | C3 |
| LCS | G ▷ C22×C439 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7902 |
Polycyclic presentation:
3,2^2,439,3|a^3=e,b^a=c,c^a=bc,d^a=d^2671764 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15804, 12);