Finite Group DatabasebetaFinite Group Databasebeta| order | 13884 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #17987775⋊C3 |
| Fitting, socle, derived, Hall | C13×C89 ⋊ C3×C4 |
| Hall | #17987775 ⋊ C3 |
| Hall | C13⋊C3×C89 ⋊ C4 |
| Sylow | C89 ⋊ Dic13⋊C3 |
| Hall | C13⋊C3 ⋊ #67063 |
| Sylow | C13 ⋊ C3×#67063 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C89 | C3×C4 |
| prime radical | C13⋊C3×D89 | C2 |
| cosocle | C13×D89 | C2×C3 |
| LCS | G ▷ C13×C89 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1157 |
Polycyclic presentation:
2,3,2,13,89|a^2=c,d^a=d^12,e^a=e^55,d^b=d^3,e^c=e^88170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13884, 18);