Finite Group DatabasebetaFinite Group Databasebeta| order | 8658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C13×C37 ⋊ C2×C32 |
| Hall | C13⋊C3×C37⋊C3 ⋊ C2 |
| Hall | D13×C37 ⋊ C32 |
| Sylow | C37 ⋊ C3×D13⋊C3 |
| Hall | D13 ⋊ C3×C37⋊C3 |
| Sylow | C13 ⋊ C2×C3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C37 | C2×C32 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
120 conjugacy classes — view the full character table.
| maximal subgroup of | #19153497⋊C3, C37⋊C3×AGL(1,𝔽13), D13⋊C3×D37⋊C3, … |
| maximal normal subgroup of | #19153497⋊C3, C37⋊C3×AGL(1,𝔽13), D13⋊C3×D37⋊C3, … |
| maximal quotient of | C37⋊C3×Dic13⋊C3, C2×D13⋊C3×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8658, 32);