Finite Group DatabasebetaFinite Group Databasebeta| order | 18590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×D169 |
| unambiguous semidirect product | C169⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (C11×D169)⋊C5 |
| Fitting, derived, Hall | C11×C169 ⋊ C2×C5 |
| Hall | C11⋊C5×C169 ⋊ C2 |
| Hall | C11×D169 ⋊ C5 |
| Sylow | C169 ⋊ C2×C11⋊C5 |
| Sylow | C11 ⋊ C5×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C11×C169 | C2×C5 |
| Frattini | C13 | D13×C11⋊C5 |
| socle | C11×C13 | C5×D13 |
| LCS | G ▷ C11×C169 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1859 |
602 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18590, 2);