Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C5 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×C5×D32 |
| Fitting, socle | C22×C33×C5 ⋊ C22 |
| derived | C32 ⋊ C24×C3×C5 |
| Hall | C33×C5 ⋊ C24 |
| Sylow | C33 ⋊ C24×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C5 | D32 |
| commutator, cosocle, hypocenter | C32 | C24×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33×C5 | C22 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C3×C5 | |
1284 conjugacy classes of subgroups; only the 416 normal subgroups are shown.
This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 416 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3×C5×GO+(4,𝔽2), C22×C3×C5×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | C22×C3×C5×GO+(4,𝔽2) |
| maximal quotient of | C22×C3×C5×((C3⋊D3)⋊C3)⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.