Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×C7×2−1+4 ⋊ C2 |
| Hall | C3×C7 ⋊ #585 |
| Sylow | C7 ⋊ #5968 |
| Sylow | C3 ⋊ #90620 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D21 |
| commutator, socle, cosocle | C2×C3×C7 | C25 |
| Fitting | C3×C7×2−1+4 | C2 |
| hypercenter | 2−1+4 | D21 |
| hypocenter | C3×C7 | #585 |
| LCS | G ▷ C2×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
1620 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 1620 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
Polycyclic presentation:
2^6,3,7|c^2=f,e^2=f,e^a=ef,g^a=g^2,h^a=h^6,d^b=df,e^c=ef204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11674);