Finite Group DatabasebetaFinite Group Databasebeta| order | 6956 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D37×D47 |
| unambiguous semidirect product | (C47×D37)⋊C2 |
| unambiguous semidirect product | (C37×D47)⋊C2 |
| unambiguous semidirect product | D1739⋊C2 |
| Fitting, socle, derived, Hall | C37×C47 ⋊ C22 |
| Sylow | C47 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C47 | C22 |
| LCS | G ▷ C37×C47 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
500 conjugacy classes — view the full character table.
| maximal subgroup of | D47×D37⋊C3, C3×D37×D47, D47×D111, … |
| maximal normal subgroup of | D47×D37⋊C3, C3×D37×D47, C5×D37×D47 |
| maximal quotient of | C3×D37×D47, D47×D111, D37×D141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6956, 8);