Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2013 |
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=g,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^52,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg760 conjugacy classes — view the full character table.
| maximal subgroup of | #27272878, #27272883, #27272888, … |
| maximal normal subgroup of | #27272878, #27272883, #27272888, … |
| maximal quotient of | #27284533, #27284547, #27284646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5593);