Finite Group DatabasebetaFinite Group Databasebeta| order | 18502 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D841 |
| unambiguous semidirect product | C841⋊(C2×C11) |
| Fitting, Hall | C11×C841 ⋊ C2 |
| derived, Sylow | C841 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D841 |
| commutator, cosocle, hypocenter | C841 | C2×C11 |
| Frattini | C29 | C11×D29 |
| Fitting | C11×C841 | C2 |
| socle | C11×C29 | D29 |
| LCS | G ▷ C841 | |
| UCS | C1 ◁ C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9251 |
4642 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#16809850, C11⋊#16809850, D11×D841, … |
| maximal normal subgroup of | C11×#16809850, C11⋊#16809850, D11×D841, … |
| maximal quotient of | C11×Dic841, C2×C11×D841 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18502, 3);