Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×C7×C3⋊Dic3 |
| derived, Sylow | C32 ⋊ C22×C4×C7 |
| Hall | C32×C7 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C7 | C3⋊D3 |
| commutator, hypocenter | C32 | C22×C4×C7 |
| Frattini | C2 | C22×C7×C3⋊D3 |
| Fitting, socle, prime radical | C23×C32×C7 | C2 |
| cosocle | C2×C32 | C23×C7 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C7 | |
324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 864);