Finite Group DatabasebetaFinite Group Databasebeta| order | 26486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D323 |
| unambiguous semidirect product | C17⋊(D19×C41) |
| unambiguous semidirect product | C19⋊(D17×C41) |
| Fitting, socle, Hall | C17×C19×C41 ⋊ C2 |
| derived, Hall | C17×C19 ⋊ C2×C41 |
| Hall | C19×C41 ⋊ D17 |
| Hall | C17×C41 ⋊ D19 |
| Sylow | C19 ⋊ D17×C41 |
| Sylow | C17 ⋊ D19×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D323 |
| commutator, cosocle, hypocenter | C17×C19 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C17×C19×C41 | C2 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 ◁ C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13243 |
6683 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26486, 7);