Finite Group DatabasebetaFinite Group Databasebeta| order | 6516 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×C181⋊C3 |
| unambiguous semidirect product | (C22×C181⋊C3)⋊C3 |
| unambiguous semidirect product | (A4×C181)⋊C3 |
| unambiguous semidirect product | (C22⋊(C181⋊C3))⋊C3 |
| Fitting, socle, derived, Hall | C22×C181 ⋊ C32 |
| Sylow | C181 ⋊ C3×A4 |
| Sylow | C22 ⋊ C3×C181⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C181 | C32 |
| LCS | G ▷ C22×C181 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
252 conjugacy classes — view the full character table.
| maximal subgroup of | A4×(C181⋊C3)⋊C5, C5×A4×C181⋊C3, A5×C181⋊C3 |
| maximal normal subgroup of | A4×(C181⋊C3)⋊C5, C5×A4×C181⋊C3 |
| maximal quotient of | C5×A4×C181⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6516, 39);