Finite Group DatabasebetaFinite Group Databasebeta| order | 8502 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×D109 |
| Fitting, socle, derived, Hall | C13×C109 ⋊ C2×C3 |
| Hall | C13⋊C3×C109 ⋊ C2 |
| Hall | C13×D109 ⋊ C3 |
| Sylow | C109 ⋊ C2×C13⋊C3 |
| Sylow | C13 ⋊ C3×D109 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C109 | C2×C3 |
| LCS | G ▷ C13×C109 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
392 conjugacy classes — view the full character table.
| maximal subgroup of | #30684287, D13⋊C3×D109, C13⋊C3×#89137, … |
| maximal normal subgroup of | #30684287, D13⋊C3×D109, C13⋊C3×#89137, … |
| maximal quotient of | C13⋊C3×Dic109, C2×C13⋊C3×D109, C13⋊C9×D109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8502, 14);