Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D41×D49 |
| unambiguous semidirect product | (C41×D49)⋊C2 |
| unambiguous semidirect product | (C49×D41)⋊C2 |
| unambiguous semidirect product | D2009⋊C2 |
| Fitting, derived, Hall | C41×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C41×C49 | C22 |
| Frattini | C7 | D7×D41 |
| socle | C7×C41 | C2×D7 |
| LCS | G ▷ C41×C49 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
572 conjugacy classes — view the full character table.
| maximal subgroup of | D41×D49⋊C3, C3×D41×D49, D41×D147, … |
| maximal normal subgroup of | D41×D49⋊C3, C3×D41×D49 |
| maximal quotient of | C3×D41×D49, D41×D147, D49×D123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 8);