Finite Group DatabasebetaFinite Group Databasebeta| order | 5700 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C19 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C19×D15 |
| unambiguous semidirect product | (C2×C3)⋊(C5×D5×C19) |
| unambiguous semidirect product | (C2×C5)⋊(C5×D3×C19) |
| Fitting, socle | C2×C3×C52×C19 ⋊ C2 |
| derived | C3×C5 ⋊ C22×C5×C19 |
| Hall | C3×C52×C19 ⋊ C22 |
| Hall | C52×C19 ⋊ C2×D3 |
| Hall | C3×C52 ⋊ C22×C19 |
| Hall | C3×C19 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D3×C19 |
| Sylow | C3 ⋊ C2×C5×D5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C19 | D15 |
| commutator, hypocenter | C3×C5 | C22×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C19 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C5×C19 | |
96 conjugacy classes of subgroups.
1710 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19×#90646, C2×C5×C19×D45, C2×C5×D15×C19⋊C3, … |
| maximal normal subgroup of | C2×C5×D15×C19⋊C3, C2×C3×C5×C19×D15 |
| maximal quotient of | C2×C5×C19×D45, C5×D3×C19×D15, C2×C5×C19×C3⋊D15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5700, 161);