Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13063703⋊C9 |
| derived, Sylow | C349 ⋊ C4×C9 |
| Hall | C349⋊C9 ⋊ C4 |
| Hall | #13063703 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #13063703⋊C3 |
| commutator, hypocenter | C349 | C4×C9 |
| Fitting, socle | C3×C349 | C3×C4 |
| prime radical, cosocle | C3×D349 | C2×C3 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,349,3|a^2=c,b^3=e,d^a=d^136,d^b=d^122,d^c=d^348123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 8);