Finite Group DatabasebetaFinite Group Databasebeta| order | 18722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C23 · Schur multiplier (H2) = C1 |
| direct product | C11×C23×D37 |
| unambiguous semidirect product | C37⋊(C2×C11×C23) |
| Fitting, socle, Hall | C11×C23×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C11×C23 |
| Hall | C23×C37 ⋊ C2×C11 |
| Hall | C11×C37 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C23 | D37 |
| commutator, cosocle, hypocenter | C37 | C2×C11×C23 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C11×C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9361 |
5060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×C23×#3866, C11×C23⋊#3866, C11×D23×D37, … |
| maximal normal subgroup of | C11×C23×#3866, C11×C23⋊#3866, C11×D23×D37, … |
| maximal quotient of | C11×C23×Dic37, C2×C11×C23×D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18722, 3);