Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| isoclinism | isoclinic class of C3⋊#1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C5 |
| direct product | C19×C3⋊#1044 |
| unambiguous semidirect product | C3⋊(C19×#1044) |
| Fitting, socle, Hall | C3×C52×C19 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C4×C19 |
| Hall | C52×C19 ⋊ Dic3 |
| Hall | C3×C19 ⋊ #1044 |
| Sylow | C52 ⋊ Dic3×C19 |
| Sylow | C3 ⋊ C19×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | C3⋊#1044 |
| commutator, hypocenter | C3×C52 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | C4 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C19 | |
64 conjugacy classes of subgroups.
456 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#11744634, C19×C9⋊#1044, C19⋊C3×C3⋊#1044, … |
| maximal normal subgroup of | C19⋊C3×C3⋊#1044, C3×C19×C3⋊#1044 |
| maximal quotient of | C19×C9⋊#1044, C3×C19×C3⋊#1044, C19×C3⋊(C3⋊#1044) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 131);