Finite Group DatabasebetaFinite Group Databasebeta| order | 5517 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C613⋊C3 |
| unambiguous semidirect product | C613⋊C32 |
| unambiguous semidirect product | (C3×C613)⋊C3 |
| Fitting, socle | C3×C613 ⋊ C3 |
| derived, Sylow | C613 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C613⋊C3 |
| commutator, hypocenter | C613 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C613 | C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
621 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D613⋊C3, C3⋊(D613⋊C3), D3×C613⋊C3, … |
| maximal normal subgroup of | C3×D613⋊C3, C3⋊(D613⋊C3), D3×C613⋊C3, … |
| maximal quotient of | C2×C3×C613⋊C3, C9×C613⋊C3, C3×#19149450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5517, 4);