Finite Group DatabasebetaFinite Group Databasebeta| order | 5526 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C307⋊C3 |
| unambiguous semidirect product | (C2×C307)⋊C32 |
| unambiguous semidirect product | (C2×C3×C307)⋊C3 |
| Fitting, socle | C2×C3×C307 ⋊ C3 |
| derived, Sylow | C307 ⋊ C2×C32 |
| Hall | C2×C307 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C307⋊C3 |
| commutator, hypocenter | C307 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C307 | C3 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
630 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5526, 13);