Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C3⋊(C7⋊(C19⋊D19)) |
| unambiguous semidirect product | C7⋊(C3⋊(C19⋊D19)) |
| unambiguous semidirect product | C19⋊D399 |
| Fitting, socle, derived, Hall | C3×C7×C192 ⋊ C2 |
| Hall | C7×C192 ⋊ D3 |
| Hall | C3×C192 ⋊ D7 |
| Sylow | C192 ⋊ D21 |
| Hall | C3×C7 ⋊ C19⋊D19 |
| Sylow | C7 ⋊ C3⋊(C19⋊D19) |
| Sylow | C3 ⋊ C7⋊(C19⋊D19) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C192 | C2 |
| LCS | G ▷ C3×C7×C192 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7581 |
Polycyclic presentation:
2,3,7,19^2|b^a=b^2,c^a=c^6,d^a=d^18,e^a=e^183792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D399, D21×C19⋊D19, D57×D133, … |
| maximal normal subgroup of | D19×D399, D21×C19⋊D19, D57×D133, … |
| maximal quotient of | C3⋊(C7⋊(C19⋊Dic19)), C2×C3⋊(C7⋊(C19⋊D19)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 90);