Finite Group DatabasebetaFinite Group Databasebeta| order | 6118 |
| isoclinism | isoclinic class of D161 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D161 |
| unambiguous semidirect product | C7⋊(C19×D23) |
| unambiguous semidirect product | C23⋊(D7×C19) |
| Fitting, socle, Hall | C7×C19×C23 ⋊ C2 |
| derived, Hall | C7×C23 ⋊ C2×C19 |
| Hall | C19×C23 ⋊ D7 |
| Hall | C7×C19 ⋊ D23 |
| Sylow | C23 ⋊ D7×C19 |
| Sylow | C7 ⋊ C19×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D161 |
| commutator, hypocenter | C7×C23 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C23 | C2 |
| LCS | G ▷ C7×C23 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
1558 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C19×D23, D19×D161, D133⋊D23, … |
| maximal normal subgroup of | D7×C19×D23, D19×D161, D133⋊D23, … |
| maximal quotient of | C19×Dic161, C2×C19×D161, C3×C19×D161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6118, 6);