Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D3×#11716029 |
| derived, Hall | C3×C72 ⋊ C22×C8 |
| Sylow | C72 ⋊ C2×D3×C8 |
| Sylow | C3 ⋊ C2×#11716029 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D72 |
| commutator, hypocenter | C3×C72 | C22×C8 |
| Fitting, cosocle | C3×C4×C72 | C23 |
| socle | C2×C3×C72 | C22×C4 |
| prime radical | C2×D3×C7⋊D7 | C4 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C4 | |
466 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×#13096284, D3×#13096368, D3×#13096364 |
| maximal normal subgroup of | D3×#13096284, D3×#13096368, D3×#13096364 |
Past the SmallGroups library coverage — no SmallGroups id.