Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q32×C53 ⋊ C2 |
| Sylow | C53 ⋊ #2264 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|b^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^52,d^b=de,e^b=ef,f^b=fg598 conjugacy classes — view the full character table.
| maximal subgroup of | #27304708, #27304713, #27304768, … |
| maximal normal subgroup of | #27304708, #27304713, #27304768, … |
| maximal quotient of | #27304529, #27304539, #27304597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6828);