Finite Group DatabasebetaFinite Group Databasebeta| order | 19065 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C41×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C3×C31)⋊(C5×C41) |
| Fitting, socle, Hall | C3×C31×C41 ⋊ C5 |
| derived, Sylow | C31 ⋊ C3×C5×C41 |
| Hall | C31×C41 ⋊ C3×C5 |
| Hall | C3×C31 ⋊ C5×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C3×C5×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C41 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3813 |
1353 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C41×ΓL(1,𝔽32), C3×D41×ΓL(1,𝔽32), C3×C41×D31⋊C5, … |
| maximal normal subgroup of | C2×C3×C41×ΓL(1,𝔽32), C3×D41×ΓL(1,𝔽32), C3×C41×D31⋊C5, … |
| maximal quotient of | C2×C3×C41×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19065, 3);