Finite Group DatabasebetaFinite Group Databasebeta| order | 8214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1369⋊C3 |
| unambiguous semidirect product | (C1369⋊C3)⋊C2 |
| Fitting, derived, Sylow | C1369 ⋊ C2×C3 |
| Hall | C1369⋊C3 ⋊ C2 |
| Hall | D1369 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C1369 | C2×C3 |
| Frattini, socle | C37 | D37⋊C3 |
| LCS | G ▷ C1369 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,37^2|c^37=d^36,c^a=c^36d,d^a=d^36,c^b=c^26d^22,d^b=d^26234 conjugacy classes — view the full character table.
| maximal subgroup of | #19129951⋊C3, C2×D1369⋊C3, #27134456⋊C2, … |
| maximal normal subgroup of | #19129951⋊C3, C2×D1369⋊C3, #27134456⋊C2, … |
| maximal quotient of | Dic1369⋊C3, C2×D1369⋊C3, #27134454⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8214, 2);