Finite Group DatabasebetaFinite Group Databasebeta| order | 18722 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C37 · Schur multiplier (H2) = C1 |
| direct product | C2×C37×C23⋊C11 |
| unambiguous semidirect product | (C2×C23)⋊(C11×C37) |
| unambiguous semidirect product | (C2×C23×C37)⋊C11 |
| Fitting, socle, Hall | C2×C23×C37 ⋊ C11 |
| derived, Sylow | C23 ⋊ C2×C11×C37 |
| Hall | C23×C37 ⋊ C2×C11 |
| Hall | C2×C23 ⋊ C11×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C2×C11×C37 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C37 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1702 |
962 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C37×C23⋊C11, Dic37×C23⋊C11, C37×Dic23⋊C11, … |
| maximal normal subgroup of | C4×C37×C23⋊C11, Dic37×C23⋊C11, C37×Dic23⋊C11, … |
| maximal quotient of | C4×C37×C23⋊C11, C22×C37×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18722, 2);