Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3×C5×#157 |
| Fitting, socle | C22×C33×C5 ⋊ C4 |
| derived | C32 ⋊ C22×C3×C4×C5 |
| Hall | C33×C5 ⋊ C22×C4 |
| Sylow | C33 ⋊ C22×C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C5 | #157 |
| commutator, hypocenter | C32 | C22×C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33×C5 | C4 |
| prime radical | C22×C3×C5×C3⋊D3 | C2 |
| cosocle | C3⋊D3 | C23×C3×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C3×C5 | |
384 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
360 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.