Finite Group DatabasebetaFinite Group Databasebeta| order | 5148 |
| isoclinism | isoclinic class of C3⋊D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊Dic39 |
| unambiguous semidirect product | C3⋊(C11×Dic39) |
| derived, Hall | C32×C13 ⋊ C4×C11 |
| Hall | C32×C11×C13 ⋊ C4 |
| Hall | C11×C13 ⋊ C3⋊Dic3 |
| Hall | C32×C11 ⋊ Dic13 |
| Sylow | C13 ⋊ C11×C3⋊Dic3 |
| Sylow | C32 ⋊ C11×Dic13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | C3⋊D39 |
| commutator, hypocenter | C32×C13 | C4×C11 |
| Frattini | C2 | C11×C3⋊D39 |
| Fitting, socle | C2×C32×C11×C13 | C2 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C2×C11 | |
72 conjugacy classes of subgroups.
1320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5148, 58);