Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of C3⋊(#41⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊(#41⋊C3) |
| unambiguous semidirect product | C3⋊(C7×#41⋊C3) |
| unambiguous semidirect product | #239⋊(C3×C7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D3×A4 |
| commutator, cosocle, hypocenter | C3×Q8 | C2×C3×C7 |
| Frattini | C2 | D3×C7×A4 |
| Fitting | C3×C7×Q8 | C2×C3 |
| socle | C2×C3×C7 | C2×A4 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C2×C7 | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 673);