Finite Group DatabasebetaFinite Group Databasebeta| order | 7844 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C53 · Schur multiplier (H2) = C2 |
| direct product | C2×C53×D37 |
| unambiguous semidirect product | C37⋊(C22×C53) |
| unambiguous semidirect product | (C2×C37)⋊(C2×C53) |
| Fitting, socle | C2×C37×C53 ⋊ C2 |
| derived, Sylow | C37 ⋊ C22×C53 |
| Hall | C37×C53 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | D37 |
| commutator, hypocenter | C37 | C22×C53 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C53 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C53 | |
20 conjugacy classes of subgroups.
2120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C53×D37⋊C3, D3×C53×D37, C2×C3×C53×D37, … |
| maximal normal subgroup of | C2×C53×D37⋊C3, C2×C3×C53×D37 |
| maximal quotient of | D3×C53×D37, C2×C3×C53×D37, C2×C53×D111 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7844, 14);