Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | #90015 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #458 |
| Sylow | C7 ⋊ C3×#458 |
320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^3,3,2^3,7|a^2=g,b^a=bf,c^a=ce,h^a=h^6,e^b=eg,f^c=fg,h^d=h^265 conjugacy classes — view the full character table.
| maximal subgroup of | #72277046, AGL(1,𝔽7)×#458, #72277128, … |
| maximal normal subgroup of | #72277046, AGL(1,𝔽7)×#458, #72277128, … |
| maximal quotient of | #72277258 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1430);