Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×Dic3×D7 |
| unambiguous semidirect product | (C3×D7)⋊C42 |
| derived, Hall | C3×C7 ⋊ C2×C42 |
| Sylow | C7 ⋊ C2×C4×Dic3 |
| Sylow | C3 ⋊ C42×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D3×D7 |
| commutator, hypocenter | C3×C7 | C2×C42 |
| Frattini | C22 | C2×D3×D7 |
| Fitting | C2×C3×C4×C7 | C22 |
| socle, cosocle | C22×C3×C7 | C23 |
| prime radical | C22×C3×D7 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C4 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C8×Dic3×D7, D7×Dic3⋊C8, #13052945, … |
| maximal normal subgroup of | C8×Dic3×D7, D7×Dic3⋊C8, #13052945, … |
| maximal quotient of | C4×D7×C3⋊C8, D7×#803, #13052351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 535);