Finite Group DatabasebetaFinite Group Databasebeta| order | 10914 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C107 · Schur multiplier (H2) = C1 |
| direct product | D51×C107 |
| unambiguous semidirect product | C3⋊(D17×C107) |
| unambiguous semidirect product | C17⋊(D3×C107) |
| Fitting, socle, Hall | C3×C17×C107 ⋊ C2 |
| derived, Hall | C3×C17 ⋊ C2×C107 |
| Hall | C17×C107 ⋊ D3 |
| Hall | C3×C107 ⋊ D17 |
| Sylow | C17 ⋊ D3×C107 |
| Sylow | C3 ⋊ D17×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C107 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C107 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C107 | |
16 conjugacy classes of subgroups.
2889 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D107, D3×D17×C107, D51⋊D107, … |
| maximal normal subgroup of | D51×D107, D3×D17×C107, D51⋊D107, … |
| maximal quotient of | C107×Dic51, C2×D51×C107, C107×D153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10914, 7);