Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×D21⋊C4 |
| derived, Hall | C3×C7 ⋊ C23×C4 |
| Sylow | C7 ⋊ C22×C4×D3 |
| Sylow | C3 ⋊ C22×C4×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×D7 |
| commutator, hypocenter | C3×C7 | C23×C4 |
| Frattini | C2 | C22×D3×D7 |
| Fitting, socle | C23×C3×C7 | C22 |
| prime radical | C23×D21 | C2 |
| cosocle | C2×C3×C7 | C24 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C23 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #13053938, #13053941, #13054247, … |
| maximal normal subgroup of | #13053938, #13053941, #13054247, … |
| maximal quotient of | C2×#10620895, C2×#10620902, C2×#10620909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1170);