Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#15688304 |
| Fitting, socle, derived | C3×C13×C19 ⋊ C3×C4 |
| Hall | C3×C19×C13⋊C3 ⋊ C4 |
| Hall | C13×C19 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ Dic19 |
| Sylow | C19 ⋊ C3⋊AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×Dic57 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C19 | C3×C4 |
| LCS | G ▷ C3×C13×C19 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,3,13,19|a^2=c,d^a=d^2,e^a=e^5,f^a=f^18,e^b=e^3,e^c=e^12237 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 180);