Finite Group DatabasebetaFinite Group Databasebeta| order | 15162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×ΓL(1,𝔽8)⋊D19 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C19×D19) |
| Fitting, socle, Hall | C7×C192 ⋊ C2×C3 |
| derived | C7×C19 ⋊ C2×C3×C19 |
| Hall | C192×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C19×D133 ⋊ C3 |
| Sylow | C192 ⋊ AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ C19×D19 |
| Sylow | C7 ⋊ C3×C19×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | ΓL(1,𝔽8)⋊D19 |
| commutator, cosocle, hypocenter | C7×C19 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C7×C192 | C2×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C19 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
988 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15162, 39);