Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#10587720⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10587720⋊D5 |
| commutator, cosocle, hypocenter | C5×C7×C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C13 | C22×C3 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C3 | |
240 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1365 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 413);