Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #3007 |
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^52,e^b=eg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27281139, #27281141, #27281251, … |
| maximal normal subgroup of | #27281139, #27281141, #27281251, … |
| maximal quotient of | #27356495, #27356534, #27356573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13770);