Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C19⋊#3874 |
| unambiguous semidirect product | (C2×C19)⋊#3874 |
| Fitting, socle | C2×C52×C19 ⋊ D3 |
| derived, Hall | C19×C52⋊C3 ⋊ C22 |
| Hall | C52×C19 ⋊ C2×D3 |
| Hall | C52⋊C3 ⋊ C2×D19 |
| Sylow | C52 ⋊ C2×D57 |
| Sylow | C19 ⋊ C2×#3874 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊#3874 |
| commutator, hypocenter | C19×C52⋊C3 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C19 | D3 |
| LCS | G ▷ C19×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C19⋊C3)⋊#3874, D3×C19⋊#3874, C2×C3×C19⋊#3874, … |
| maximal normal subgroup of | C2×(C19⋊C3)⋊#3874, C2×C3×C19⋊#3874 |
| maximal quotient of | C2×C19⋊#90646, D3×C19⋊#3874, C2×C3×C19⋊#3874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 101);