Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| isoclinism | isoclinic class of C3⋊AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×C3⋊AGL(1,𝔽13) |
| unambiguous semidirect product | C3⋊(C19×AGL(1,𝔽13)) |
| unambiguous semidirect product | (C3⋊#261)⋊(C3×C19) |
| Fitting, socle | C3×C13×C19 ⋊ C3×C4 |
| derived | C3×C13 ⋊ C3×C4×C19 |
| Hall | C3×C19×C13⋊C3 ⋊ C4 |
| Hall | C13×C19 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ C4×C19 |
| Sylow | C13 ⋊ C3×Dic3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C3⋊AGL(1,𝔽13) |
| commutator, hypocenter | C3×C13 | C3×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C19 | C3×C4 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C19 | |
56 conjugacy classes of subgroups.
399 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 175);