Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| automorphism | Aut(G) order 6750240 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4018 |
| direct product | C2×D2009 |
| unambiguous semidirect product | (C2×C41)⋊D49 |
| unambiguous semidirect product | (C2×C49)⋊D41 |
| Fitting | C2×C41×C49 ⋊ C2 |
| derived, Hall | C41×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2009 |
| commutator, hypocenter | C41×C49 | C22 |
| Frattini | C7 | C2×D287 |
| Fitting | C2×C41×C49 | C2 |
| socle | C2×C7×C41 | D7 |
| LCS | G ▷ C41×C49 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
2012 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C41⋊(D49⋊C3), D3×D2009, C2×C3×D2009, … |
| maximal normal subgroup of | C2×C41⋊(D49⋊C3), C2×C3×D2009, D8036 |
| maximal quotient of | D3×D2009, C2×C3×D2009, C2×D6027, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 11);