Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3107 |
390 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=g,b^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^52,f^c=fg1078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27278809, #27278811, #27278816, … |
| maximal normal subgroup of | #27278809, #27278811, #27278816, … |
| maximal quotient of | #27384129, #27387031, #27387053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14581);