Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| isoclinism | isoclinic class of D111 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D111 |
| unambiguous semidirect product | C3⋊(C49×D37) |
| unambiguous semidirect product | C37⋊(D3×C49) |
| Fitting, Hall | C3×C37×C49 ⋊ C2 |
| derived, Hall | C3×C37 ⋊ C2×C49 |
| Hall | C37×C49 ⋊ D3 |
| Hall | C3×C49 ⋊ D37 |
| Sylow | C37 ⋊ D3×C49 |
| Sylow | C3 ⋊ C49×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D111 |
| commutator, hypocenter | C3×C37 | C2×C49 |
| Frattini | C7 | C7×D111 |
| Fitting | C3×C37×C49 | C2 |
| socle, cosocle | C3×C7×C37 | C2×C7 |
| prime radical | C7×D111 | C7 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 ◁ C49 | |
24 conjugacy classes of subgroups.
2793 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C49×D37, D49×D111, D111⋊D49, … |
| maximal normal subgroup of | D3×C49×D37, D49×D111, D111⋊D49, … |
| maximal quotient of | C49×Dic111, C2×C49×D111, C49×D333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 22);