Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×C49×D37 |
| Fitting, Hall | C3×C37×C49 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C3×C49 |
| Hall | C37×C49 ⋊ C2×C3 |
| Hall | C3×C37 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C49 | D37 |
| commutator, hypocenter | C37 | C2×C3×C49 |
| Frattini | C7 | C3×C7×D37 |
| Fitting | C3×C37×C49 | C2 |
| socle | C3×C7×C37 | C2×C7 |
| prime radical | C3×C7×D37 | C7 |
| cosocle | C7×C37 | C2×C3×C7 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C49 | |
24 conjugacy classes of subgroups.
2940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C49×#3866, C3×C49⋊#3866, C3×D37×D49, … |
| maximal normal subgroup of | C3×C49×#3866, C3×C49⋊#3866, C3×D37×D49, … |
| maximal quotient of | C3×C49×Dic37, C2×C3×C49×D37, C9×C49×D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 18);