Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic1365 |
| unambiguous semidirect product | C7⋊(C3⋊Dic195) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D1365 |
| commutator, hypocenter | C32×C5×C7×C13 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C5×C7×C13 | C2 |
| LCS | G ▷ C32×C5×C7×C13 | |
| UCS | C1 ◁ C2 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16380 |
Polycyclic presentation:
2,3^2,5,7,13,2|a^2=g,b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^124098 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 332);