Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#11716115 |
| Fitting | C22×C3×C72 ⋊ C23 |
| Hall | C3×C72 ⋊ C22×D4 |
| Sylow | C72 ⋊ C2×D3×D4 |
| Sylow | C3 ⋊ C2×#11716115 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D72 |
| commutator, socle, cosocle | C2×C3×C72 | C24 |
| Fitting | C22×C3×C72 | C23 |
| hypercenter | C22 | D3×D72 |
| hypocenter | C3×C72 | C22×D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C2 ◁ C22 | |
1346 conjugacy classes of subgroups.
228 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210376, #72222259, C2×D3×#11716115, … |
| maximal normal subgroup of | D3×#72210376, C2×D3×#11716115, D3×D4×D72, … |
| maximal quotient of | #72222259, C2×D3×#11716115, D3×#13096368, … |
Past the SmallGroups library coverage — no SmallGroups id.