Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊(D13⋊C9))⋊D7 |
| unambiguous semidirect product | ((C13⋊C9)⋊D7)⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C5⋊(D13⋊C3))⋊D7 |
| commutator, hypocenter | C5×C7×C13 | C22×C9 |
| Fitting, socle, cosocle | C3×C5×C7×C13 | C22×C3 |
| prime radical | C3×D35⋊D13 | C3 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4095 |
Polycyclic presentation:
2^2,3,5,7,13,3|c^3=g,e^a=e^6,f^a=f^12,d^b=d^4,e^b=e^6,f^c=f^3294 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 124);