Finite Group DatabasebetaFinite Group Databasebeta| order | 8214 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C2×C37×C37⋊C3 |
| unambiguous semidirect product | (C2×C37)⋊(C3×C37) |
| Fitting, socle, Hall | C2×C372 ⋊ C3 |
| derived | C37 ⋊ C2×C3×C37 |
| Sylow | C372 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | C37⋊C3 |
| commutator, hypocenter | C37 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C2×C372 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C37 | |
40 conjugacy classes of subgroups.
1110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×Dic37⋊C3, #30656057, C37⋊C3×Dic37, … |
| maximal normal subgroup of | C37×Dic37⋊C3, #30656057, C37⋊C3×Dic37, … |
| maximal quotient of | C4×C37×C37⋊C3, C22×C37×C37⋊C3, C2×C37×#66524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8214, 16);