Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D95 |
| unambiguous semidirect product | (C5×D5)⋊(C3×D19) |
| Fitting, socle, Hall | C3×C52×C19 ⋊ C22 |
| derived, Hall | C52×C19 ⋊ C22×C3 |
| Hall | C3×C52 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ D52 |
| Sylow | C52 ⋊ C2×C3×D19 |
| Sylow | C19 ⋊ C3×D52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D95 |
| commutator, hypocenter | C52×C19 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C19 | C22 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
588 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C5⋊(#4294⋊C2), C9×D5×D95, C3×D5×C5⋊(D19⋊C3), … |
| maximal normal subgroup of | D5×C5⋊(#4294⋊C2), C9×D5×D95, C3×D5×C5⋊(D19⋊C3), … |
| maximal quotient of | C9×D5×D95, C32×D5×D95, C3×D5×D285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 119);