Finite Group DatabasebetaFinite Group Databasebeta| order | 19206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D97⋊C9) |
| unambiguous semidirect product | (C97⋊C9)⋊D11 |
| unambiguous semidirect product | D1067⋊C9 |
| derived, Hall | C11×C97 ⋊ C2×C9 |
| Hall | C11×C97⋊C9 ⋊ C2 |
| Hall | D1067 ⋊ C9 |
| Hall | C97⋊C9 ⋊ D11 |
| Sylow | C97 ⋊ C9×D11 |
| Sylow | C11 ⋊ D97⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊(D97⋊C3) |
| commutator, hypocenter | C11×C97 | C2×C9 |
| Fitting, socle, cosocle | C3×C11×C97 | C2×C3 |
| prime radical | C3×D1067 | C3 |
| LCS | G ▷ C11×C97 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9603 |
Polycyclic presentation:
2,3,11,97,3|b^3=e,c^a=c^10,d^a=d^96,d^b=d^35591 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D97⋊C9, C2×C11⋊(D97⋊C9) |
| maximal normal subgroup of | D11×D97⋊C9, C2×C11⋊(D97⋊C9) |
| maximal quotient of | C11⋊(Dic97⋊C9), C2×C11⋊(D97⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19206, 12);