Finite Group DatabasebetaFinite Group Databasebeta| order | 19162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | D13×C67⋊C11 |
| unambiguous semidirect product | C13⋊(C2×C67⋊C11) |
| unambiguous semidirect product | (D13×C67)⋊C11 |
| Fitting, socle, derived, Hall | C13×C67 ⋊ C2×C11 |
| Hall | C13×C67⋊C11 ⋊ C2 |
| Hall | D13×C67 ⋊ C11 |
| Sylow | C67 ⋊ C11×D13 |
| Sylow | C13 ⋊ C2×C67⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C67 | C2×C11 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 871 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | (C67⋊C11)⋊#261, #261×C67⋊C11, D13×D67⋊C11, … |
| maximal normal subgroup of | (C67⋊C11)⋊#261, #261×C67⋊C11, D13×D67⋊C11, … |
| maximal quotient of | Dic13×C67⋊C11, C2×D13×C67⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19162, 11);