Finite Group DatabasebetaFinite Group Databasebeta| order | 8658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C13⋊C3×D37 |
| Fitting, socle | C3×C13×C37 ⋊ C2×C3 |
| derived, Hall | C13×C37 ⋊ C2×C32 |
| Hall | C3×C37×C13⋊C3 ⋊ C2 |
| Hall | C13×D37 ⋊ C32 |
| Sylow | C37 ⋊ C2×C3×C13⋊C3 |
| Sylow | C13 ⋊ C32×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C13⋊C3×D37 |
| commutator, hypocenter | C13×C37 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C37 | C2×C3 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
420 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19153508, C3×D37×D13⋊C3, C3×C13⋊C3×#3866, … |
| maximal normal subgroup of | C3×#19153508, C3×D37×D13⋊C3, C3×C13⋊C3×#3866, … |
| maximal quotient of | C3×C13⋊C3×Dic37, C2×C3×C13⋊C3×D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8658, 51);