Finite Group DatabasebetaFinite Group Databasebeta| order | 5418 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D7⋊C9 |
| unambiguous semidirect product | D7⋊(C9×C43) |
| unambiguous semidirect product | (C7⋊C9)⋊(C2×C43) |
| derived, Sylow | C7 ⋊ C2×C9×C43 |
| Hall | C43×C7⋊C9 ⋊ C2 |
| Hall | D7×C43 ⋊ C9 |
| Hall | C7×C43 ⋊ C2×C9 |
| Hall | C7⋊C9 ⋊ C2×C43 |
| Hall | D7 ⋊ C9×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C43 | AGL(1,𝔽7) |
| commutator, hypocenter | C7 | C2×C9×C43 |
| Frattini | C3 | AGL(1,𝔽7)×C43 |
| Fitting, socle | C3×C7×C43 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C43 | |
24 conjugacy classes of subgroups.
903 conjugacy classes — view the full character table.
| maximal subgroup of | D43×D7⋊C9, C2×C43×D7⋊C9, C5×C43×D7⋊C9, … |
| maximal normal subgroup of | D43×D7⋊C9, C2×C43×D7⋊C9, C5×C43×D7⋊C9, … |
| maximal quotient of | C43×Dic7⋊C9, C2×C43×D7⋊C9, C5×C43×D7⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5418, 14);