Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #2950 |
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 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=f,b^2=g,c^2=fg,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^23,e^b=eg,d^c=dg,h^c=h^30,h^f=h^52226 conjugacy classes — view the full character table.
| maximal subgroup of | #28311505, #28311523, #28311657, … |
| maximal normal subgroup of | #28311505, #28311523, #28311657, … |
| maximal quotient of | #28316417, #28316418, #28316419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21271);