Finite Group DatabasebetaFinite Group Databasebeta| order | 5658 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C41×D23 |
| unambiguous semidirect product | C23⋊(C2×C3×C41) |
| Fitting, socle, Hall | C3×C23×C41 ⋊ C2 |
| derived, Sylow | C23 ⋊ C2×C3×C41 |
| Hall | C23×C41 ⋊ C2×C3 |
| Hall | C3×C23 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | D23 |
| commutator, hypocenter | C23 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C41 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C3×C41 | |
16 conjugacy classes of subgroups.
1599 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D23×D41, D3×C41×D23, D23×D123, … |
| maximal normal subgroup of | C3×D23×D41, D3×C41×D23, D23×D123, … |
| maximal quotient of | C3×C41×Dic23, C2×C3×C41×D23, C9×C41×D23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5658, 3);