Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#13183634 |
| Fitting, socle | C2×C3×C72 ⋊ C22×C3 |
| derived | C3×C72 ⋊ C23×C3 |
| Hall | C3×#3861 ⋊ C23 |
| Sylow | C72 ⋊ C22×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13183634 |
| commutator, cosocle, hypocenter | C3×C72 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C72 | C22×C3 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C2 | |
366 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
66 conjugacy classes — view the full character table.
| maximal subgroup of | #72222115, #72222121, C2×D3×#64423⋊C2, … |
| maximal normal subgroup of | #72222115, #72222121, C2×D3×#64423⋊C2, … |
| maximal quotient of | #72222121, D3×#13183634, C2×C3×#13183634, … |
Past the SmallGroups library coverage — no SmallGroups id.