Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C33 |
| direct product | C22×C3⋊(C3⋊ΓL(1,𝔽16)) |
| Fitting, socle | C22×C33×C5 ⋊ C4 |
| derived, Hall | C33×C5 ⋊ C22×C4 |
| Sylow | C33 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22×C3⋊(C3⋊Dic3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊(C3⋊ΓL(1,𝔽16)) |
| commutator, hypocenter | C33×C5 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33×C5 | C4 |
| prime radical | C22×C33×D5 | C2 |
| cosocle | C33×D5 | C23 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C22 | |
1512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 540 |
228 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3⋊D3×ΓL(1,𝔽16), C22×D3×C3⋊ΓL(1,𝔽16), C22×AGL(1,𝔽5)×C3⋊(C3⋊D3) |
| maximal normal subgroup of | C22×C3⋊D3×ΓL(1,𝔽16), C22×D3×C3⋊ΓL(1,𝔽16), C22×AGL(1,𝔽5)×C3⋊(C3⋊D3) |
Past the SmallGroups library coverage — no SmallGroups id.