Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| automorphism | Aut(G) order 2645136 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1413 |
| unambiguous semidirect product | C9⋊Dic157 |
| derived, Hall | C9×C157 ⋊ C4 |
| Sylow | C157 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1413 |
| commutator, hypocenter | C9×C157 | C4 |
| Frattini | C2×C3 | D471 |
| Fitting | C2×C9×C157 | C2 |
| socle | C2×C3×C157 | D3 |
| LCS | G ▷ C9×C157 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,157,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^156,e^a=e^21416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic1413, Dic7065, C9⋊#15691171, … |
| maximal normal subgroup of | C5×Dic1413, Dic2826 |
| maximal quotient of | C5×Dic1413, Dic7065, C9⋊#15691171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 6);