Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C3×C7 ⋊ C22 |
| Hall | C3×C7 ⋊ B(4,𝔽2) |
| Sylow | C7 ⋊ #5032 |
| Sylow | C3 ⋊ #89804 |
396 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
Polycyclic presentation:
2^6,3,7|c^a=ce,d^a=df,h^a=h^6,c^b=cd,e^b=ef,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#5032, D3×#89804, #72244296, … |
| maximal normal subgroup of | D7×#5032, D3×#89804, #72244296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4193);