Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #1733 |
404 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^52,c^b=cg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289411, #27289412, #27289416, … |
| maximal normal subgroup of | #27289411, #27289412, #27289416, … |
| maximal quotient of | #27273530, #27273536, #27273539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4221);