Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C121⋊#261) |
| unambiguous semidirect product | C121⋊(C3⋊#261) |
| Fitting, derived, Hall | C3×C13×C121 ⋊ C4 |
| Hall | C13×C121 ⋊ Dic3 |
| Hall | C3×C121 ⋊ #261 |
| Sylow | C121 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ Dic121 |
| Sylow | C13 ⋊ Dic363 |
| Sylow | C3 ⋊ C121⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C13×C121 | C4 |
| Frattini | C11 | C3⋊(C11⋊#261) |
| socle | C3×C11×C13 | Dic11 |
| prime radical | C3×C11×D13 | D11 |
| cosocle | C3×D13×C121 | C2 |
| LCS | G ▷ C3×C13×C121 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4719 |
Polycyclic presentation:
2^2,3,11,13,11|a^2=b,d^11=f^10,c^a=c^2,d^a=d^10f,e^a=e^8,f^a=f^10,e^b=e^121455 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 23);