Finite Group DatabasebetaFinite Group Databasebeta| order | 19026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C151⋊C9)⋊D7 |
| derived, Hall | C7×C151 ⋊ C2×C9 |
| Hall | C7×C151⋊C9 ⋊ C2 |
| Hall | D1057 ⋊ C9 |
| Hall | C151⋊C9 ⋊ D7 |
| Sylow | C151 ⋊ C9×D7 |
| Sylow | C7 ⋊ D151⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C151⋊C3)⋊D7 |
| commutator, hypocenter | C7×C151 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C151 | C2×C3 |
| prime radical | C3×D1057 | C3 |
| LCS | G ▷ C7×C151 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9513 |
Polycyclic presentation:
2,3,7,151,3|b^3=e,c^a=c^6,d^a=d^150,d^b=d^32570 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D151⋊C9, C2×(C151⋊C9)⋊D7 |
| maximal normal subgroup of | D7×D151⋊C9, C2×(C151⋊C9)⋊D7 |
| maximal quotient of | (C151⋊C9)⋊Dic7, C2×(C151⋊C9)⋊D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19026, 21);