Finite Group DatabasebetaFinite Group Databasebeta| order | 7596 |
| automorphism | Aut(G) order 4785480 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1899 |
| unambiguous semidirect product | C9⋊Dic211 |
| unambiguous semidirect product | C211⋊Dic9 |
| derived, Hall | C9×C211 ⋊ C4 |
| Sylow | C211 ⋊ Dic9 |
| Sylow | C9 ⋊ Dic211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1899 |
| commutator, hypocenter | C9×C211 | C4 |
| Frattini | C2×C3 | D633 |
| Fitting | C2×C9×C211 | C2 |
| socle | C2×C3×C211 | D3 |
| LCS | G ▷ C9×C211 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,211,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^210,e^a=e^21902 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic1899, Dic9495, C9⋊(Dic211⋊C5), … |
| maximal normal subgroup of | C5×Dic1899, C9⋊(Dic211⋊C5), Dic3798 |
| maximal quotient of | C5×Dic1899, Dic9495, C9⋊(C211⋊AGL(1,𝔽5)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7596, 6);