Finite Group DatabasebetaFinite Group Databasebeta| order | 7479 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×C277⋊C3 |
| unambiguous semidirect product | C277⋊C33 |
| unambiguous semidirect product | (C3×C277)⋊C32 |
| Fitting, socle | C32×C277 ⋊ C3 |
| derived, Sylow | C277 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C277⋊C3 |
| commutator, hypocenter | C277 | C33 |
| Frattini | C1 | G |
| Fitting, socle | C32×C277 | C3 |
| LCS | G ▷ C277 | |
| UCS | C1 ◁ C32 | |
56 conjugacy classes of subgroups.
855 conjugacy classes — view the full character table.
| maximal subgroup of | (C3×C277⋊C3)⋊C9, #36376235, #36376237, … |
| maximal normal subgroup of | (C3×C277⋊C3)⋊C9, #36376235, #36376237, … |
| maximal quotient of | C3×C9×C277⋊C3, C32×C277⋊C9, H(3,𝔽3)×C277⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7479, 13);