Finite Group DatabasebetaFinite Group Databasebeta| order | 5439 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C37⋊C3 |
| unambiguous semidirect product | C37⋊(C3×C72) |
| Fitting, socle, Hall | C72×C37 ⋊ C3 |
| derived, Sylow | C37 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C37⋊C3 |
| commutator, hypocenter | C37 | C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
735 conjugacy classes — view the full character table.
| maximal subgroup of | C72×D37⋊C3, C7×(C37⋊C3)⋊D7, C7×D7×C37⋊C3, … |
| maximal normal subgroup of | C72×D37⋊C3, C7×(C37⋊C3)⋊D7, C7×D7×C37⋊C3, … |
| maximal quotient of | C2×C72×C37⋊C3, C72×#66524, C3×C72×C37⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5439, 7);