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 ⋊ #1740 |
420 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,c^2=g,b^a=bd,d^a=dg,e^b=eg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27289304, #27289305, #27289553, … |
| maximal normal subgroup of | #27289304, #27289305, #27289553, … |
| maximal quotient of | #27273682, #27273688, #27273694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4242);