Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4⋊C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1296 |
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 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.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=f,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^30,c^b=cg,h^d=h^52298 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289594, #28300982, #28300985, … |
| maximal normal subgroup of | C2×#20289594, #28300982, #28300985, … |
| maximal quotient of | #28298024, #28298040, #28298041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19389);