Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D19×#3874 |
| Fitting, socle, Hall | C52×C19 ⋊ C2×D3 |
| derived, Hall | C19×C52⋊C3 ⋊ C22 |
| Hall | C52⋊C3 ⋊ C2×D19 |
| Sylow | C52 ⋊ D3×D19 |
| Sylow | C19 ⋊ C2×#3874 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C19×C52⋊C3 | C22 |
| Fitting, socle | C52×C19 | C2×D3 |
| LCS | G ▷ C19×C52⋊C3 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
143 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×#3874, C3×D19×#3874, D19×C3⋊#3874, … |
| maximal normal subgroup of | D19⋊C3×#3874, C3×D19×#3874 |
| maximal quotient of | D19×#90646, C3×D19×#3874, D19×C3⋊#3874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 86);