Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3084 |
376 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=eg,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^52,f^c=fg760 conjugacy classes — view the full character table.
| maximal subgroup of | #27441632, #27441635, #27441641, … |
| maximal normal subgroup of | #27441632, #27441635, #27441641, … |
| maximal quotient of | #27383617, #27385094, #27385136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 14370);