Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of D63 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×C7⋊(C9⋊C8) |
| unambiguous semidirect product | (C2×C7)⋊(C9⋊C8) |
| unambiguous semidirect product | (C2×C9)⋊(C7⋊C8) |
| derived, Hall | C7×C9 ⋊ C2×C8 |
| Sylow | C9 ⋊ C2×C7⋊C8 |
| Sylow | C7 ⋊ C2×C9⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D63 |
| commutator, hypocenter | C7×C9 | C2×C8 |
| Frattini | C3×C4 | C2×D21 |
| Fitting | C2×C4×C7×C9 | C2 |
| socle, prime radical | C22×C3×C7 | Dic3 |
| cosocle | C4×C7×C9 | C22 |
| LCS | G ▷ C7×C9 | |
| UCS | C1 ◁ C2×C4 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 95);