Finite Group DatabasebetaFinite Group Databasebeta| order | 672 |
| isoclinism | isoclinic class of A4×AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C2 |
| direct product | A4×AGL(1,𝔽8) |
| unambiguous semidirect product | C22⋊(C3×AGL(1,𝔽8)) |
| unambiguous semidirect product | (C23×A4)⋊C7 |
| Fitting, socle, derived, Sylow | C25 ⋊ C3×C7 |
| Hall | C22×AGL(1,𝔽8) ⋊ C3 |
| Hall | C23×A4 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C25 | C3×C7 |
| LCS | G ▷ C25 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
32 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(672, 1258);