Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic285 |
| unambiguous semidirect product | C3⋊(C5×Dic95) |
| unambiguous semidirect product | C19⋊(C5×Dic15) |
| derived | C3×C5×C19 ⋊ C4×C5 |
| Hall | C3×C52×C19 ⋊ C4 |
| Hall | C52×C19 ⋊ Dic3 |
| Hall | C3×C52 ⋊ Dic19 |
| Hall | C3×C19 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ Dic57 |
| Sylow | C19 ⋊ C5×Dic15 |
| Sylow | C3 ⋊ C5×Dic95 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D285 |
| commutator, hypocenter | C3×C5×C19 | C4×C5 |
| Frattini | C2 | C5×D285 |
| Fitting, socle | C2×C3×C52×C19 | C2 |
| LCS | G ▷ C3×C5×C19 | |
| UCS | C1 ◁ C2×C5 | |
64 conjugacy classes of subgroups.
1440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19⋊#11744607, C5×Dic855, C5×C3⋊((C19⋊C3)⋊Dic5), … |
| maximal normal subgroup of | C5×C3⋊((C19⋊C3)⋊Dic5), C3×C5×Dic285 |
| maximal quotient of | C5×Dic855, C3×C5×Dic285, C5×C3⋊Dic285 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 66);