Finite Group DatabasebetaFinite Group Databasebeta| order | 15747 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C181⋊C3 |
| unambiguous semidirect product | C181⋊(C3×C29) |
| unambiguous semidirect product | (C29×C181)⋊C3 |
| Fitting, socle, Hall | C29×C181 ⋊ C3 |
| derived, Sylow | C181 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C181⋊C3 |
| commutator, cosocle, hypocenter | C181 | C3×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C181 | C3 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C29 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5249 |
1827 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C29×C181⋊C3, C29×D181⋊C3, D29×C181⋊C3, … |
| maximal normal subgroup of | C2×C29×C181⋊C3, C29×D181⋊C3, D29×C181⋊C3, … |
| maximal quotient of | C2×C29×C181⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15747, 1);