Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D285 |
| unambiguous semidirect product | (C3×D5)⋊D95 |
| unambiguous semidirect product | (C5×D5)⋊D57 |
| unambiguous semidirect product | (D5×C19)⋊D15 |
| Fitting, socle, derived, Hall | C3×C52×C19 ⋊ C22 |
| Hall | C52×C19 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ D52 |
| Sylow | C52 ⋊ C2×D57 |
| Sylow | C19 ⋊ D5×D15 |
| Sylow | C3 ⋊ D5×D95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C19 | C22 |
| LCS | G ▷ C3×C52×C19 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
576 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D855, D5×C3⋊(C5⋊(D19⋊C3)), #3874⋊D57, … |
| maximal normal subgroup of | D5×C3⋊(C5⋊(D19⋊C3)), C3×D5×D285 |
| maximal quotient of | D5×D855, C3×D5×D285, D5×C3⋊D285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 141);