Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊(Dic13⋊C3)) |
| derived, Hall | C112×C13 ⋊ C3×C4 |
| Hall | C11⋊Dic143 ⋊ C3 |
| Hall | C112×C13⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ Dic13⋊C3 |
| Hall | C13⋊C3 ⋊ C11⋊Dic11 |
| Sylow | C13 ⋊ C3×C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C11⋊(C11⋊(D13⋊C3)) |
| commutator, hypocenter | C112×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C112×C13 | C2×C3 |
| prime radical | C2×C112×C13⋊C3 | C2 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 ◁ C2 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6292 |
Polycyclic presentation:
2,3,11^2,13,2|a^2=f,c^a=c^10,d^a=d^10,e^a=e^12,e^b=e^3856 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 45);