Finite Group DatabasebetaFinite Group Databasebeta| order | 5460 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊#63118 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C13 | C3×C4 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,7,13|a^2=c,d^a=d^4,e^a=e^6,f^a=f^5,e^b=e^2,f^c=f^12109 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5460, 100);