Finite Group DatabasebetaFinite Group Databasebeta| order | 15330 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(ΓL(1,𝔽8)⋊D73) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D365 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C73 | C2×C3 |
| LCS | G ▷ C5×C7×C73 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2555 |
Polycyclic presentation:
2,3,5,7,73|c^a=c^4,d^a=d^6,e^a=e^72,d^b=d^2917 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15330, 46);