Finite Group DatabasebetaFinite Group Databasebeta| order | 8214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C37⋊C3)⋊D37 |
| Fitting, socle, derived, Sylow | C372 ⋊ C2×C3 |
| Hall | C37×C37⋊C3 ⋊ C2 |
| Hall | C37⋊D37 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C372 | C2×C3 |
| LCS | G ▷ C372 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,37^2|c^a=c^36,d^a=d^36,c^b=c^26282 conjugacy classes — view the full character table.
| maximal subgroup of | #30656076, #30656077, D37×D37⋊C3, … |
| maximal normal subgroup of | #30656076, #30656077, D37×D37⋊C3, … |
| maximal quotient of | #30656057, C2×(C37⋊C3)⋊D37, #66524⋊D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8214, 10);