Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1292 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^52,d^b=dg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270801, #27270802, #27270804, … |
| maximal normal subgroup of | #27270801, #27270802, #27270804, … |
| maximal quotient of | #27270630, #27270635, #27270697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2385);