Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | D4×Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #3278 |
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,h^b=h^52,e^d=eg679 conjugacy classes — view the full character table.
| maximal subgroup of | #27373530, #27373532, #27373545, … |
| maximal normal subgroup of | #27373530, #27373532, #27373545, … |
| maximal quotient of | #27375421, #27375537, #27375667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 16172);