Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of A4×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C22×A4×D7 |
| Fitting, socle | C24×C7 ⋊ C2×C3 |
| derived | C22×C7 ⋊ C23×C3 |
| Hall | C24×D7 ⋊ C3 |
| Sylow | C7 ⋊ C23×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | A4×D7 |
| commutator, cosocle, hypocenter | C22×C7 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C7 | C2×C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C22 | |
356 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1267);