Finite Group DatabasebetaFinite Group Databasebeta| order | 5382 |
| isoclinism | isoclinic class of D117 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D117 |
| unambiguous semidirect product | C9⋊(C23×D13) |
| unambiguous semidirect product | C13⋊(D9×C23) |
| Fitting, Hall | C9×C13×C23 ⋊ C2 |
| derived, Hall | C9×C13 ⋊ C2×C23 |
| Hall | C13×C23 ⋊ D9 |
| Hall | C9×C23 ⋊ D13 |
| Sylow | C13 ⋊ D9×C23 |
| Sylow | C9 ⋊ C23×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D117 |
| commutator, hypocenter | C9×C13 | C2×C23 |
| Frattini | C3 | C23×D39 |
| Fitting | C9×C13×C23 | C2 |
| socle | C3×C13×C23 | D3 |
| LCS | G ▷ C9×C13 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
1380 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C23×D117, C23×D585, C7×C23×D117, … |
| maximal normal subgroup of | C5×C23×D117, C7×C23×D117 |
| maximal quotient of | C5×C23×D117, C23×D585, C7×C23×D117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5382, 11);