Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| isoclinism | isoclinic class of #67194 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×#67194 |
| Fitting, socle | C2×C33×C5 ⋊ C8 |
| derived | C32×C5 ⋊ C2×C3×C8 |
| Hall | C33×C5 ⋊ C2×C8 |
| Sylow | C33 ⋊ C2×#168 |
| Sylow | C5 ⋊ C2×C3×AGL(1,𝔽9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #67194 |
| commutator, hypocenter | C32×C5 | C2×C3×C8 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C5 | C8 |
| prime radical | C2×C3×C5×C3⋊D3 | C4 |
| cosocle | C5×#157 | C22×C3 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C2×C3 | |
116 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
126 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×D5×AGL(1,𝔽9), AGL(1,𝔽7)×#67194, C2×C3×PSU(3,𝔽2)⋊D5, … |
| maximal normal subgroup of | C2×C3×D5×AGL(1,𝔽9), C2×C3×PSU(3,𝔽2)⋊D5, C2×C3×#10624311 |
| maximal quotient of | AGL(1,𝔽7)×#67194 |
Past the SmallGroups library coverage — no SmallGroups id.