Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊AGL(1,𝔽13)) |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C3×C4 |
| Hall | C11⋊(C11⋊#261) ⋊ C3 |
| Hall | C112×C13⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ AGL(1,𝔽13) |
| Hall | C13⋊C3 ⋊ C11⋊Dic11 |
| Sylow | C13 ⋊ C3×C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C112×C13 | C3×C4 |
| prime radical | C112×D13⋊C3 | C2 |
| cosocle | C112×D13 | C2×C3 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1573 |
Polycyclic presentation:
2,3,2,11^2,13|a^2=c,d^a=d^10,e^a=e^10,f^a=f^5,f^b=f^3,f^c=f^12493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 73);