Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C3⋊((C19⋊C3)⋊C4) |
| unambiguous semidirect product | C3⋊(C13×(C19⋊C3)⋊C4) |
| unambiguous semidirect product | (C19⋊C3)⋊(Dic3×C13) |
| unambiguous semidirect product | Dic57⋊(C3×C13) |
| derived | C3×C19 ⋊ C3×C4×C13 |
| Hall | C3×C13×C19⋊C3 ⋊ C4 |
| Hall | C13×C19 ⋊ C3×Dic3 |
| Hall | C3×C19⋊C3 ⋊ C4×C13 |
| Sylow | C19 ⋊ C3×Dic3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | C3⋊(D19⋊C3) |
| commutator, hypocenter | C3×C19 | C3×C4×C13 |
| Frattini | C2 | C13×C3⋊(D19⋊C3) |
| Fitting, socle | C2×C3×C13×C19 | C2×C3 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C2×C13 | |
56 conjugacy classes of subgroups.
468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 106);