Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C19 |
| direct product | C7×C3⋊(C19⋊D19) |
| unambiguous semidirect product | C3⋊(C7×C19⋊D19) |
| unambiguous semidirect product | C19⋊(C7×D57) |
| Fitting, socle, Hall | C3×C7×C192 ⋊ C2 |
| derived, Hall | C3×C192 ⋊ C2×C7 |
| Hall | C7×C192 ⋊ D3 |
| Sylow | C192 ⋊ D3×C7 |
| Hall | C3×C7 ⋊ C19⋊D19 |
| Sylow | C3 ⋊ C7×C19⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(C19⋊D19) |
| commutator, cosocle, hypocenter | C3×C192 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C192 | C2 |
| LCS | G ▷ C3×C192 | |
| UCS | C1 ◁ C7 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7581 |
3801 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D19×D57, D3×C7×C19⋊D19, D133⋊D57, … |
| maximal normal subgroup of | C7×D19×D57, D3×C7×C19⋊D19, D133⋊D57, … |
| maximal quotient of | C7×C3⋊(C19⋊Dic19), C2×C7×C3⋊(C19⋊D19) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 93);