Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C157 · Schur multiplier (H2) = C1 |
| direct product | Dic9×C157 |
| unambiguous semidirect product | C9⋊(C4×C157) |
| derived, Sylow | C9 ⋊ C4×C157 |
| Hall | C9×C157 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C157 | D9 |
| commutator, hypocenter | C9 | C4×C157 |
| Frattini | C2×C3 | D3×C157 |
| Fitting | C2×C9×C157 | C2 |
| socle | C2×C3×C157 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C157 | |
18 conjugacy classes of subgroups.
1884 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic9×C157, C157×Dic45, C157×C9⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C5×Dic9×C157 |
| maximal quotient of | C5×Dic9×C157, C157×Dic45, C157×C9⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 4);