Finite Group DatabasebetaFinite Group Databasebeta| order | 4620 |
| automorphism | Aut(G) order 1108800 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1155 |
| unambiguous semidirect product | C3⋊Dic385 |
| unambiguous semidirect product | C7⋊Dic165 |
| unambiguous semidirect product | C11⋊Dic105 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1155 |
| commutator, hypocenter | C3×C5×C7×C11 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C7×C11 | C2 |
| LCS | G ▷ C3×C5×C7×C11 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 4620 |
Polycyclic presentation:
2,3,5,7,11,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^101158 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4620, 19);