Finite Group DatabasebetaFinite Group Databasebeta| order | 18590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C11×C132 ⋊ C2×C5 |
| derived | C11×C13 ⋊ C2×C5×C13 |
| Hall | C132×C11⋊C5 ⋊ C2 |
| Hall | C13×D143 ⋊ C5 |
| Sylow | C132 ⋊ AGL(1,𝔽11) |
| Hall | C11⋊C5 ⋊ C13×D13 |
| Sylow | C11 ⋊ C5×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C13⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11×C13 | C2×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C132 | C2×C5 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C13 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 286 |
689 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18590, 15);