Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#384 ⋊ C2 |
| Sylow | C53 ⋊ #2094 |
290 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 91 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=dg,b^2=deg,d^2=g,e^2=g,b^a=bd,c^a=ce,h^a=h^52,c^b=cf,d^b=dg,e^b=eg,h^b=h^52,d^c=dg,e^c=eg,h^c=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27273349, #27273352, #27273354, … |
| maximal normal subgroup of | #27273349, #27273352, #27273354, … |
| maximal quotient of | #27289076, #27289104, #27289137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6044);