Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#19129741 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C13 | C3×C4 |
| prime radical | C3×D5×#63270 | C2 |
| cosocle | C3×C7×D5×C13 | C2×C3 |
| LCS | G ▷ C3×C5×C7×C13 | |
| UCS | C1 | |
112 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1365 |
Polycyclic presentation:
2,3,2,3,5,7,13|a^2=c,d^a=d^2,e^a=e^2,g^a=g^12,f^b=f^2,g^b=g^3,e^c=e^4213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 489);