Finite Group DatabasebetaFinite Group Databasebeta| order | 6118 |
| isoclinism | isoclinic class of D133 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D133 |
| unambiguous semidirect product | C7⋊(C23×D19) |
| unambiguous semidirect product | C19⋊(D7×C23) |
| Fitting, socle, Hall | C7×C19×C23 ⋊ C2 |
| derived, Hall | C7×C19 ⋊ C2×C23 |
| Hall | C19×C23 ⋊ D7 |
| Hall | C7×C23 ⋊ D19 |
| Sylow | C19 ⋊ D7×C23 |
| Sylow | C7 ⋊ C23×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D133 |
| commutator, hypocenter | C7×C19 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C23 | C2 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
1564 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D133, D7×C23×D19, D133⋊D23, … |
| maximal normal subgroup of | D23×D133, D7×C23×D19, D133⋊D23, … |
| maximal quotient of | C23×Dic133, C2×C23×D133, C3×C23×D133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6118, 7);