Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Hall | #90019 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #379 |
| Sylow | C7 ⋊ C3×#379 |
1012 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 184 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,h^d=h^2116 conjugacy classes — view the full character table.
| maximal subgroup of | #72218345, #120×ΓL(1,𝔽8)⋊C4, C4×#10620789, … |
| maximal normal subgroup of | #120×ΓL(1,𝔽8)⋊C4, C4×#10620789, AGL(1,𝔽7)×#379, … |
| maximal quotient of | #72218345, #72230185, #72230204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1436);