Finite Group DatabasebetaFinite Group Databasebeta| order | 26010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D289 |
| unambiguous semidirect product | C289⋊(C2×C32×C5) |
| Fitting, Hall | C32×C5×C289 ⋊ C2 |
| derived, Sylow | C289 ⋊ C2×C32×C5 |
| Hall | C32×C289 ⋊ C2×C5 |
| Hall | C5×C289 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | D289 |
| commutator, cosocle, hypocenter | C289 | C2×C32×C5 |
| Frattini | C17 | C32×C5×D17 |
| Fitting | C32×C5×C289 | C2 |
| socle | C32×C5×C17 | D17 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C32×C5 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13005 |
6570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26010, 10);