Finite Group DatabasebetaFinite Group Databasebeta| order | 10362 |
| isoclinism | isoclinic class of C157⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C11×C157⋊C3 |
| unambiguous semidirect product | (C2×C157)⋊(C3×C11) |
| unambiguous semidirect product | (C2×C11×C157)⋊C3 |
| Fitting, socle, Hall | C2×C11×C157 ⋊ C3 |
| derived, Sylow | C157 ⋊ C2×C3×C11 |
| Hall | C11×C157 ⋊ C2×C3 |
| Hall | C2×C157 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | C157⋊C3 |
| commutator, cosocle, hypocenter | C157 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C157 | C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C11 | |
16 conjugacy classes of subgroups.
1210 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10362, 2);