Finite Group DatabasebetaFinite Group Databasebeta| order | 5382 |
| isoclinism | isoclinic class of D69 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D69 |
| unambiguous semidirect product | C3⋊(C3×C13×D23) |
| unambiguous semidirect product | C23⋊(C3×D3×C13) |
| Fitting, socle, Hall | C32×C13×C23 ⋊ C2 |
| derived | C3×C23 ⋊ C2×C3×C13 |
| Hall | C13×C23 ⋊ C3×D3 |
| Hall | C32×C23 ⋊ C2×C13 |
| Hall | C32×C13 ⋊ D23 |
| Sylow | C23 ⋊ C3×D3×C13 |
| Sylow | C32 ⋊ C13×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D69 |
| commutator, hypocenter | C3×C23 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C23 | C2 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C3×C13 | |
36 conjugacy classes of subgroups.
1404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C13×D69, C3×C13×D345, C13×C3⋊(ΓL(1,𝔽8)⋊D23), … |
| maximal normal subgroup of | C3×C5×C13×D69, C3×C7×C13×D69 |
| maximal quotient of | C3×C5×C13×D69, C3×C13×D345, C13×C3⋊(ΓL(1,𝔽8)⋊D23), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5382, 26);