Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×D3×D72 |
| Fitting | C3×C4×C72 ⋊ C23 |
| derived, Hall | C3×C72 ⋊ C23×C4 |
| Sylow | C72 ⋊ C22×C4×D3 |
| Sylow | C3 ⋊ C2×C4×D72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×D72 |
| commutator, hypocenter | C3×C72 | C23×C4 |
| Frattini | C2 | C2×D3×D72 |
| Fitting | C3×C4×C72 | C23 |
| socle, cosocle | C2×C3×C72 | C24 |
| prime radical | C2×D3×D72 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C4 | |
1106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D4×D72, D3×#13096688, D3×#13096694 |
| maximal normal subgroup of | D3×D4×D72, D3×#13096688, D3×#13096694 |
Past the SmallGroups library coverage — no SmallGroups id.