Finite Group DatabasebetaFinite Group Databasebeta| order | 19026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3171 |
| unambiguous semidirect product | C7⋊(C3⋊D453) |
| unambiguous semidirect product | C151⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C151 ⋊ C2 |
| Hall | C32×C151 ⋊ D7 |
| Hall | C7×C151 ⋊ C3⋊D3 |
| Sylow | C151 ⋊ C3⋊D21 |
| Hall | C32×C7 ⋊ D151 |
| Sylow | C32 ⋊ D1057 |
| Sylow | C7 ⋊ C3⋊D453 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C151 | C2 |
| LCS | G ▷ C32×C7×C151 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9513 |
Polycyclic presentation:
2,3^2,7,151|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^1504758 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D3171, D21×D453, C3⋊D21×D151, … |
| maximal normal subgroup of | D3×D3171, D21×D453, C3⋊D21×D151, … |
| maximal quotient of | C3⋊Dic3171, C2×C3⋊D3171 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19026, 62);