Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×C3⋊(C7⋊C8) |
| derived, Hall | C3×C7 ⋊ C82 |
| Sylow | C7 ⋊ C8×C3⋊C8 |
| Sylow | C3 ⋊ C8×C7⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D21 |
| commutator, hypocenter | C3×C7 | C82 |
| Frattini | C42 | C2×D21 |
| Fitting | C3×C4×C7×C8 | C2 |
| socle, prime radical | C22×C3×C7 | C42 |
| cosocle | C3×C42×C7 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C4×C8 | |
148 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, 646);