Finite Group DatabasebetaFinite Group Databasebeta| order | 10584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C3⋊D3×#3861 |
| Fitting, socle | C22×C32×C72 ⋊ C2×C3 |
| derived | C32×C72 ⋊ C23×C3 |
| Hall | C32×#3861 ⋊ C23 |
| Sylow | C72 ⋊ C22×C3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊D3×#3861 |
| commutator, cosocle, hypocenter | C32×C72 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C72 | C2×C3 |
| LCS | G ▷ C32×C72 | |
| UCS | C1 ◁ C22 | |
2320 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 2320 conjugacy classes of subgroups — too many to draw. Only its 451 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
456 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3⋊D3×#64424, #72222214 |
| maximal normal subgroup of | C22×C3⋊D3×#64424, #72222214 |
Past the SmallGroups library coverage — no SmallGroups id.