Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×#10596873 |
| derived, Sylow | C72 ⋊ C2×C32×C4 |
| Hall | C3×#3861 ⋊ C2×C4 |
| Hall | C2×C7×Dic7 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #64423 |
| commutator, hypocenter | C72 | C2×C32×C4 |
| Frattini | C2 | C2×C3×#64423 |
| Fitting, socle | C22×C3×C72 | C2×C3 |
| prime radical | C22×C3×#3861 | C2 |
| cosocle | C2×C72 | C22×C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C22×C3 | |
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#11924174, C2×D3×#10596873, C2×#72222048, … |
| maximal normal subgroup of | C2×C3×#11924174, C2×D3×#10596873, C2×#72222048, … |
Past the SmallGroups library coverage — no SmallGroups id.