Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| direct product | D5×C13×C3⋊AGL(1,𝔽7) |
| unambiguous semidirect product | (C3×D5)⋊(C13×AGL(1,𝔽7)) |
| unambiguous semidirect product | (D5×ΓL(1,𝔽8))⋊(D3×C13) |
| unambiguous semidirect product | (D5×D21)⋊(C3×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D5×C3⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C3×C5×C7 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C13 | C22×C3 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C13 | |
176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1365 |
624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 536);