Finite Group DatabasebetaFinite Group Databasebeta| order | 3528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×C3⋊#64424 |
| Fitting | C3×C4×C72 ⋊ C2×C3 |
| derived | C3×C72 ⋊ C2×C3×C4 |
| Hall | C3×#3861 ⋊ C2×C4 |
| Sylow | C72 ⋊ C3×C4×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C3⋊#64424 |
| commutator, hypocenter | C3×C72 | C2×C3×C4 |
| Frattini | C2 | C2×C3⋊#64424 |
| Fitting | C3×C4×C72 | C2×C3 |
| socle, cosocle | C2×C3×C72 | C22×C3 |
| prime radical | C2×C3⋊#64424 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C4 | |
350 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 588 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#64424, C2×C4×C3⋊#64424, D4×C3⋊#64424, … |
| maximal normal subgroup of | C4×D3×#64424, C2×C4×C3⋊#64424, D4×C3⋊#64424, … |
| maximal quotient of | C2×C4×C3⋊#64424 |
Past the SmallGroups library coverage — no SmallGroups id.