Finite Group DatabasebetaFinite Group Databasebeta| order | 26274 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D453 |
| unambiguous semidirect product | C3⋊(C29×D151) |
| unambiguous semidirect product | C151⋊(D3×C29) |
| Fitting, socle, Hall | C3×C29×C151 ⋊ C2 |
| derived, Hall | C3×C151 ⋊ C2×C29 |
| Hall | C29×C151 ⋊ D3 |
| Sylow | C151 ⋊ D3×C29 |
| Hall | C3×C29 ⋊ D151 |
| Sylow | C3 ⋊ C29×D151 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D453 |
| commutator, cosocle, hypocenter | C3×C151 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C151 | C2 |
| LCS | G ▷ C3×C151 | |
| UCS | C1 ◁ C29 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13137 |
6612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26274, 7);