Finite Group DatabasebetaFinite Group Databasebeta| order | 8658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#16864525 |
| derived, Hall | C13×C37 ⋊ C2×C9 |
| Hall | C2×C13×C37 ⋊ C9 |
| Hall | C2×C37 ⋊ C13⋊C9 |
| Sylow | C37 ⋊ C2×C13⋊C9 |
| Hall | C2×C13 ⋊ #66524 |
| Sylow | C13 ⋊ C2×#66524 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #13089649 |
| commutator, hypocenter | C13×C37 | C2×C9 |
| Frattini | C3 | C2×#13089649 |
| Fitting, socle | C2×C3×C13×C37 | C3 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
978 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#16864525, #31772740, #31772744, … |
| maximal normal subgroup of | C4×#16864525, #31772740, #31772744, … |
| maximal quotient of | C4×#16864525, C22×#16864525 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8658, 5);