Finite Group DatabasebetaFinite Group Databasebeta| order | 5460 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊Dic65 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(ΓL(1,𝔽8)⋊D13) |
| commutator, hypocenter | C5×C7×C13 | C3×C4 |
| Fitting, socle | C2×C5×C7×C13 | C2×C3 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,13,2|a^2=f,c^a=c^4,d^a=d^6,e^a=e^12,d^b=d^2334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5460, 46);