Finite Group DatabasebetaFinite Group Databasebeta| order | 8294 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C29 · Schur multiplier (H2) = C1 |
| direct product | C11×D13×C29 |
| unambiguous semidirect product | C13⋊(C2×C11×C29) |
| Fitting, socle, Hall | C11×C13×C29 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C11×C29 |
| Hall | C13×C29 ⋊ C2×C11 |
| Hall | C11×C13 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C29 | D13 |
| commutator, hypocenter | C13 | C2×C11×C29 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C29 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C11×C29 | |
16 conjugacy classes of subgroups.
2552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C29×#261, C11×#13094089, C11×D13×D29, … |
| maximal normal subgroup of | C11×C29×#261, C11×#13094089, C11×D13×D29, … |
| maximal quotient of | C11×C29×Dic13, C2×C11×D13×C29, C3×C11×D13×C29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8294, 3);