Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊(C349⋊C9) |
| unambiguous semidirect product | C349⋊(C22⋊C9) |
| derived, Hall | C22×C349 ⋊ C9 |
| Sylow | C349 ⋊ C22⋊C9 |
| Sylow | C22 ⋊ C349⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C349⋊C3) |
| commutator, hypocenter | C22×C349 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C349 | C3 |
| LCS | G ▷ C22×C349 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
3,2^2,349,3|a^3=e,b^a=c,c^a=bc,d^a=d^1221404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 15);