Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #19129727 |
| commutator, hypocenter | C5×C7×C13 | C4×C9 |
| Fitting, socle | C3×C5×C7×C13 | C3×C4 |
| prime radical, cosocle | C3×C7×D65 | C2×C3 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4095 |
Polycyclic presentation:
2,3,2,5,7,13,3|a^2=c,b^3=g,d^a=d^2,e^a=e^6,f^a=f^8,e^b=e^2,f^b=f^3,d^c=d^4,f^c=f^12162 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 69);