Finite Group DatabasebetaFinite Group Databasebeta| order | 8164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#10597845 |
| Fitting, socle, Hall | C13×C157 ⋊ C4 |
| derived, Sylow | C157 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #10597845 |
| commutator, hypocenter | C157 | C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C157 | C4 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C13 | |
12 conjugacy classes of subgroups.
559 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#10597845⋊C3, #37587616, #37587617, … |
| maximal normal subgroup of | C13×#10597845⋊C3, #37587616, #37587617, … |
| maximal quotient of | C3×C13×#10597845, C13×C3⋊#10597845 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8164, 11);