Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C7×#95 ⋊ C2 |
| Hall | C3×C7 ⋊ #397 |
| Sylow | C7 ⋊ #4675 |
| Sylow | C3 ⋊ #89447 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D21 |
| commutator, socle, cosocle | C23×C3×C7 | C23 |
| Fitting | C3×C7×#95 | C2 |
| prime radical | C23×D21 | C22 |
| hypercenter | #95 | D21 |
| hypocenter | C3×C7 | #397 |
| LCS | G ▷ C23×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C23 ◁ #95 | |
340 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
Polycyclic presentation:
2^6,3,7|b^2=e,c^2=f,b^a=bf,c^a=cef,g^a=g^2,h^a=h^6,c^b=cd222 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5602);