Finite Group DatabasebetaFinite Group Databasebeta| order | 8658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C2×C13×C37 ⋊ C32 |
| derived, Hall | C13×C37 ⋊ C2×C32 |
| Hall | C2×C37 ⋊ C3×C13⋊C3 |
| Sylow | C37 ⋊ C2×C3×C13⋊C3 |
| Hall | C2×C13 ⋊ C3×C37⋊C3 |
| Sylow | C13 ⋊ C2×C3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊C3×C37⋊C3 |
| commutator, hypocenter | C13×C37 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C37 | C32 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
210 conjugacy classes — view the full character table.
| maximal subgroup of | #19153486⋊C3, C37⋊C3×Dic13⋊C3, C13⋊C3×Dic37⋊C3, … |
| maximal normal subgroup of | #19153486⋊C3, C37⋊C3×Dic13⋊C3, C13⋊C3×Dic37⋊C3, … |
| maximal quotient of | C4×C13⋊C3×C37⋊C3, C22×C13⋊C3×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8658, 41);