Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C13 | C32×C4 |
| prime radical | C5×ΓL(1,𝔽8)×D13⋊C3 | C2 |
| cosocle | C5×C7×D13 | C2×C32 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 | |
144 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 455 |
Polycyclic presentation:
2,3^2,2,5,7,13|a^2=d,e^a=e^4,f^a=f^6,g^a=g^5,g^b=g^3,f^c=f^2,g^d=g^12127 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 345);