Finite Group DatabasebetaFinite Group Databasebeta| order | 8658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#15668368 |
| Fitting, socle | C3×C13×C37 ⋊ C2×C3 |
| derived, Hall | C13×C37 ⋊ C2×C32 |
| Hall | C3×#13089649 ⋊ C2 |
| Hall | D481 ⋊ C32 |
| Sylow | C37 ⋊ C3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15668368 |
| 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.
258 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19153494, C3×#19153496, C3×#15668360⋊C2, … |
| maximal normal subgroup of | C3×#19153494, C3×#19153496, C3×#15668360⋊C2, … |
| maximal quotient of | C3×#19153489, C2×C3×#15668368 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8658, 45);