Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1736 |
448 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,d^2=g,f^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 | #27289421, #27289422, #27289455, … |
| maximal normal subgroup of | #27289421, #27289422, #27289455, … |
| maximal quotient of | #27273555, #27273565, #27273577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4231);