Finite Group DatabasebetaFinite Group Databasebeta| order | 30228 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊#11745021) |
| unambiguous semidirect product | C11⋊(C3⋊#11745021) |
| Fitting, socle, derived, Hall | C3×C11×C229 ⋊ C4 |
| Hall | C11×C229 ⋊ Dic3 |
| Hall | C3×C229 ⋊ Dic11 |
| Sylow | C229 ⋊ Dic33 |
| Hall | C3×C11 ⋊ #11745021 |
| Sylow | C11 ⋊ C3⋊#11745021 |
| Sylow | C3 ⋊ C11⋊#11745021 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C229 | C4 |
| prime radical, cosocle | C3×C11×D229 | C2 |
| LCS | G ▷ C3×C11×C229 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7557 |
Polycyclic presentation:
2^2,3,11,229|a^2=b,c^a=c^2,d^a=d^10,e^a=e^122,e^b=e^2281917 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30228, 25);