Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1461 |
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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=e,b^2=f,c^2=fg,e^2=g,b^a=bd,d^a=df,e^b=ef,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27274654, C8×#13133135, #27274664, … |
| maximal normal subgroup of | #27274654, C8×#13133135, #27274664, … |
| maximal quotient of | #27272063, #27272069, #27272071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2833);