Finite Group DatabasebetaFinite Group Databasebeta| order | 8892 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3 |
| direct product | C3×C4×C13×C19⋊C3 |
| unambiguous semidirect product | (C4×C19)⋊(C32×C13) |
| unambiguous semidirect product | (C3×C4×C19)⋊(C3×C13) |
| Fitting | C3×C4×C13×C19 ⋊ C3 |
| derived, Sylow | C19 ⋊ C32×C4×C13 |
| Hall | C4×C13×C19 ⋊ C32 |
| Hall | C13×C19 ⋊ C32×C4 |
| Hall | C4×C19 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4×C13 | C19⋊C3 |
| commutator, hypocenter | C19 | C32×C4×C13 |
| Frattini | C2 | C2×C3×C13×C19⋊C3 |
| Fitting | C3×C4×C13×C19 | C3 |
| socle | C2×C3×C13×C19 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C4×C13 | |
72 conjugacy classes of subgroups.
1404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8892, 122);