Finite Group DatabasebetaFinite Group Databasebeta| order | 4356 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic363 |
| unambiguous semidirect product | C121⋊(C3⋊Dic3) |
| derived, Hall | C32×C121 ⋊ C4 |
| Sylow | C121 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ Dic121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D363 |
| commutator, hypocenter | C32×C121 | C4 |
| Frattini | C2×C11 | C3⋊D33 |
| Fitting, cosocle | C2×C32×C121 | C2 |
| socle, prime radical | C2×C32×C11 | D11 |
| LCS | G ▷ C32×C121 | |
| UCS | C1 ◁ C2 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4356 |
Polycyclic presentation:
2,3^2,11,2,11|a^2=e,d^11=f^10,b^a=b^2,c^a=c^2,d^a=d^10f,f^a=f^101092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4356, 16);