Finite Group DatabasebetaFinite Group Databasebeta| order | 8658 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#15668363 |
| Fitting, socle, derived | C3×C13×C37 ⋊ C2×C3 |
| Hall | C3×#13089650 ⋊ C2 |
| Hall | C13×C37 ⋊ C3×D3 |
| Sylow | C37 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ D3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C37 | C2×C3 |
| LCS | G ▷ C3×C13×C37 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,13,37|c^a=c^2,d^a=d^12,d^b=d^3,e^b=e^26267 conjugacy classes — view the full character table.
| maximal subgroup of | #15668359⋊D3, #15668367⋊D3, D3×#15668363, … |
| maximal normal subgroup of | #15668359⋊D3, #15668367⋊D3, D3×#15668363, … |
| maximal quotient of | C3⋊#19153484, C2×C3⋊#15668363 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8658, 59);