Finite Group DatabasebetaFinite Group Databasebeta| order | 6027 |
| isoclinism | isoclinic class of C49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×C49⋊C3 |
| unambiguous semidirect product | C49⋊(C3×C41) |
| unambiguous semidirect product | (C41×C49)⋊C3 |
| Fitting, Hall | C41×C49 ⋊ C3 |
| derived, Sylow | C49 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C49⋊C3 |
| commutator, hypocenter | C49 | C3×C41 |
| Frattini | C7 | ΓL(1,𝔽8)×C41 |
| Fitting | C41×C49 | C3 |
| socle | C7×C41 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C41 | |
12 conjugacy classes of subgroups.
779 conjugacy classes — view the full character table.
| maximal subgroup of | D41×C49⋊C3, C41×D49⋊C3, C41⋊(D49⋊C3), … |
| maximal normal subgroup of | D41×C49⋊C3, C41×D49⋊C3, C41⋊(D49⋊C3), … |
| maximal quotient of | C2×C41×C49⋊C3, C41×C49⋊C9, C3×C41×C49⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6027, 2);