Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C7 ⋊ #336 |
| Sylow | C7 ⋊ #4524 |
| Sylow | C3 ⋊ #89345 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22×C4 | D3×D7 |
| commutator | C2×C3×C7 | C4×C8 |
| Fitting, cosocle | C22×C3×C4×C7 | C22 |
| socle, prime radical | C23×C3×C7 | C2×C4 |
| hypocenter | C3×C7 | #336 |
| LCS | G ▷ C2×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C22×C4 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1344 |
Polycyclic presentation:
2^6,3,7|a^2=e,b^2=c,c^2=f,b^a=bd,h^a=h^6,g^b=g^2216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 283);