Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of A4×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C3 |
| derived | C22×C7 ⋊ C32×C4 |
| Hall | C22×Dic7 ⋊ C32 |
| Sylow | C7 ⋊ C3×C4×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×AGL(1,𝔽7) |
| commutator, hypocenter | C22×C7 | C32×C4 |
| Fitting, socle, cosocle | C23×C7 | C2×C32 |
| prime radical | C2×A4×ΓL(1,𝔽8) | C2 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C2 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 526);