Finite Group DatabasebetaFinite Group Databasebeta| order | 15477 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C11 · Schur multiplier (H2) = C1 |
| direct product | C7×(C67⋊C3)⋊C11 |
| unambiguous semidirect product | (C67⋊C3)⋊(C7×C11) |
| unambiguous semidirect product | (C67⋊C11)⋊(C3×C7) |
| unambiguous semidirect product | (C7×C67⋊C3)⋊C11 |
| Fitting, socle, Hall | C7×C67 ⋊ C3×C11 |
| derived, Sylow | C67 ⋊ C3×C7×C11 |
| Hall | C7×C67⋊C11 ⋊ C3 |
| Hall | C7×C67⋊C3 ⋊ C11 |
| Hall | C67⋊C11 ⋊ C3×C7 |
| Hall | C67⋊C3 ⋊ C7×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C67⋊C3)⋊C11 |
| commutator, cosocle, hypocenter | C67 | C3×C7×C11 |
| Frattini | C1 | G |
| Fitting, socle | C7×C67 | C3×C11 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 469 |
245 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C7×(C67⋊C3)⋊C11, C7×AGL(1,𝔽67), D7×(C67⋊C3)⋊C11, … |
| maximal normal subgroup of | C2×C7×(C67⋊C3)⋊C11, C7×AGL(1,𝔽67), D7×(C67⋊C3)⋊C11, … |
| maximal quotient of | C2×C7×(C67⋊C3)⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15477, 7);