Finite Group DatabasebetaFinite Group Databasebeta| order | 18590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C132 · Schur multiplier (H2) = C13 |
| direct product | C2×C132×C11⋊C5 |
| unambiguous semidirect product | (C2×C11)⋊(C5×C132) |
| unambiguous semidirect product | (C2×C11×C13)⋊(C5×C13) |
| unambiguous semidirect product | (C2×C11×C132)⋊C5 |
| Fitting, socle, Hall | C2×C11×C132 ⋊ C5 |
| derived, Sylow | C11 ⋊ C2×C5×C132 |
| Hall | C11×C132 ⋊ C2×C5 |
| Hall | C2×C11 ⋊ C5×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C132 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C2×C5×C132 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C132 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C132 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3718 |
2366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18590, 19);