Finite Group DatabasebetaFinite Group Databasebeta| order | 26505 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C19 · Schur multiplier (H2) = C3 |
| direct product | C32×C19×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C32×C31)⋊(C5×C19) |
| unambiguous semidirect product | (C32×C19×C31)⋊C5 |
| Fitting, socle, Hall | C32×C19×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C32×C5×C19 |
| Hall | C19×C31 ⋊ C32×C5 |
| Hall | C32×C31 ⋊ C5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C19 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C32×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C19×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C32×C19 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5301 |
1881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26505, 24);