Finite Group DatabasebetaFinite Group Databasebeta| order | 26010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×D153 |
| unambiguous semidirect product | C9⋊(C5×C17×D17) |
| unambiguous semidirect product | C17⋊(C5×C17×D9) |
| Fitting, Hall | C5×C9×C172 ⋊ C2 |
| derived | C9×C17 ⋊ C2×C5×C17 |
| Hall | C9×C172 ⋊ C2×C5 |
| Hall | C5×C172 ⋊ D9 |
| Sylow | C172 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ C17×D17 |
| Sylow | C9 ⋊ C5×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | D153 |
| commutator, cosocle, hypocenter | C9×C17 | C2×C5×C17 |
| Frattini | C3 | C5×C17×D51 |
| Fitting | C5×C9×C172 | C2 |
| socle | C3×C5×C172 | D3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C5×C17 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1530 |
6630 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26010, 34);