Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| isoclinism | isoclinic class of D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D37⋊C3 |
| unambiguous semidirect product | D37⋊(C3×C49) |
| unambiguous semidirect product | (C37⋊C3)⋊(C2×C49) |
| Fitting, Hall | C37×C49 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C2×C3×C49 |
| Hall | C49×C37⋊C3 ⋊ C2 |
| Hall | C49×D37 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C49 |
| Hall | D37 ⋊ C3×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D37⋊C3 |
| commutator, hypocenter | C37 | C2×C3×C49 |
| Frattini | C7 | C7×D37⋊C3 |
| Fitting | C37×C49 | C2×C3 |
| socle, cosocle | C7×C37 | C2×C3×C7 |
| prime radical | C7×D37⋊C3 | C7 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
588 conjugacy classes — view the full character table.
| maximal subgroup of | C49×#3866⋊C3, #36344183, D49×D37⋊C3, … |
| maximal normal subgroup of | C49×#3866⋊C3, #36344183, D49×D37⋊C3, … |
| maximal quotient of | C49×Dic37⋊C3, C2×C49×D37⋊C3, C49×#66524⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 2);