Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C19×#1042 |
| Fitting, socle, Hall | C3×C52×C19 ⋊ C4 |
| derived, Sylow | C52 ⋊ C3×C4×C19 |
| Hall | C52×C19 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | #1042 |
| commutator, hypocenter | C52 | C3×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | C4 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C19 | |
52 conjugacy classes of subgroups.
741 conjugacy classes — view the full character table.
| maximal subgroup of | #1042×#4294, C9×C19×#1042, C3×C19⋊C3×#1042, … |
| maximal normal subgroup of | #1042×#4294, C9×C19×#1042, C3×C19⋊C3×#1042, … |
| maximal quotient of | C9×C19×#1042, C32×C19×#1042, C3×C19×C3⋊#1042 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 115);