Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(C7⋊C32) |
| unambiguous semidirect product | (C2×C3)⋊(C7⋊C32) |
| unambiguous semidirect product | (C2×C7)⋊(C3⋊C32) |
| derived, Hall | C3×C7 ⋊ C2×C32 |
| Sylow | C7 ⋊ C2×C3⋊C32 |
| Sylow | C3 ⋊ C2×C7⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D21 |
| commutator, hypocenter | C3×C7 | C2×C32 |
| Frattini | C16 | C2×D21 |
| Fitting | C2×C3×C7×C16 | C2 |
| socle, prime radical | C22×C3×C7 | C16 |
| cosocle | C3×C7×C16 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C16 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 691);