Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C32×ΓL(1,𝔽16) |
| Fitting, socle | C22×C33×C5 ⋊ C4 |
| derived | C3×C5 ⋊ C22×C32×C4 |
| Hall | C33×C5 ⋊ C22×C4 |
| Sylow | C33 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22×C32×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C22×C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33×C5 | C4 |
| prime radical | C22×C33×D5 | C2 |
| cosocle | C3×D5 | C23×C32 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C22×C32 | |
904 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 360 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3⋊D3×ΓL(1,𝔽16), C22×C32×D3×AGL(1,𝔽5), C22×ΓL(1,𝔽16)⋊(C3⋊D3) |
| maximal normal subgroup of | C22×C3⋊D3×ΓL(1,𝔽16), C22×C32×D3×AGL(1,𝔽5), C22×ΓL(1,𝔽16)⋊(C3⋊D3) |
Past the SmallGroups library coverage — no SmallGroups id.