Finite Group DatabasebetaFinite Group Databasebeta| order | 26505 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×C19⋊C3×ΓL(1,𝔽32) |
| unambiguous semidirect product | C19⋊(C32×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C3×C19)⋊(C3×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C3×C31×C19⋊C3)⋊C5 |
| Fitting, socle | C3×C19×C31 ⋊ C3×C5 |
| derived, Hall | C19×C31 ⋊ C32×C5 |
| Hall | C3×C31×C19⋊C3 ⋊ C5 |
| Hall | C19×ΓL(1,𝔽32) ⋊ C32 |
| Sylow | C31 ⋊ C3×C5×C19⋊C3 |
| Sylow | C19 ⋊ C32×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C19⋊C3×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C19×C31 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C31 | C3×C5 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1767 |
297 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26505, 19);