Finite Group DatabasebetaFinite Group Databasebeta| order | 5460 |
| automorphism | Aut(G) order 1572480 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1365 |
| unambiguous semidirect product | C3⋊Dic455 |
| unambiguous semidirect product | C7⋊Dic195 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1365 |
| commutator, hypocenter | C3×C5×C7×C13 | C4 |
| Fitting, socle | C2×C3×C5×C7×C13 | C2 |
| LCS | G ▷ C3×C5×C7×C13 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,13,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^121368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic4095, C3⋊#19129705, C3⋊#19129706, … |
| maximal normal subgroup of | C3⋊#19129705, C3⋊#19129706, C3⋊(ΓL(1,𝔽8)⋊Dic65), … |
| maximal quotient of | Dic4095, C3×Dic1365, C3⋊Dic1365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5460, 20);