Finite Group DatabasebetaFinite Group Databasebeta| order | 5394 |
| isoclinism | isoclinic class of D93 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D93 |
| unambiguous semidirect product | C3⋊(C29×D31) |
| unambiguous semidirect product | C31⋊(D3×C29) |
| Fitting, socle, Hall | C3×C29×C31 ⋊ C2 |
| derived, Hall | C3×C31 ⋊ C2×C29 |
| Hall | C29×C31 ⋊ D3 |
| Hall | C3×C29 ⋊ D31 |
| Sylow | C31 ⋊ D3×C29 |
| Sylow | C3 ⋊ C29×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D93 |
| commutator, hypocenter | C3×C31 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C31 | C2 |
| LCS | G ▷ C3×C31 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
1392 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C29×D279, C29×C3⋊(D31⋊C3), C29×C3⋊D93, … |
| maximal normal subgroup of | C29×C3⋊(D31⋊C3), C3×C29×D93, C5×C29×D93, … |
| maximal quotient of | C29×D279, C29×C3⋊D93, C3×C29×D93, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5394, 7);