Finite Group DatabasebetaFinite Group Databasebeta| order | 7134 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C3×C29×D41 |
| unambiguous semidirect product | C41⋊(C2×C3×C29) |
| Fitting, socle, Hall | C3×C29×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C3×C29 |
| Hall | C29×C41 ⋊ C2×C3 |
| Hall | C3×C41 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C29 | D41 |
| commutator, hypocenter | C41 | C2×C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C41 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C29 | |
16 conjugacy classes of subgroups.
1914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C29×#4223, C3×#18011703, C3×D29×D41, … |
| maximal normal subgroup of | C3×C29×#4223, C3×#18011703, C3×D29×D41, … |
| maximal quotient of | C3×C29×Dic41, C2×C3×C29×D41, C9×C29×D41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7134, 2);