Finite Group DatabasebetaFinite Group Databasebeta| order | 18538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D403 |
| unambiguous semidirect product | C13⋊(C23×D31) |
| unambiguous semidirect product | C31⋊(C23×D13) |
| Fitting, socle, Hall | C13×C23×C31 ⋊ C2 |
| derived, Hall | C13×C31 ⋊ C2×C23 |
| Hall | C23×C31 ⋊ D13 |
| Hall | C13×C23 ⋊ D31 |
| Sylow | C31 ⋊ C23×D13 |
| Sylow | C13 ⋊ C23×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D403 |
| commutator, cosocle, hypocenter | C13×C31 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C13×C23×C31 | C2 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9269 |
4669 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D13×D31, D23×D403, D299⋊D31, … |
| maximal normal subgroup of | C23×D13×D31, D23×D403, D299⋊D31, … |
| maximal quotient of | C23×Dic403, C2×C23×D403 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18538, 6);