Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×C8×D21 |
| Fitting | C32×C7×C8 ⋊ C2 |
| derived | C3×C7 ⋊ C2×C3×C8 |
| Hall | C32×C7 ⋊ C2×C8 |
| Sylow | C32 ⋊ C8×D7 |
| Sylow | C7 ⋊ C3×D3×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | D21 |
| commutator, hypocenter | C3×C7 | C2×C3×C8 |
| Frattini | C4 | C2×C3×D21 |
| Fitting | C32×C7×C8 | C2 |
| socle | C2×C32×C7 | C2×C4 |
| prime radical | C2×C3×D21 | C4 |
| cosocle | C3×C4×C7 | C22×C3 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C3×C8 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 442);