Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C53 ⋊ #2911 |
492 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=f,b^2=e,d^2=g,e^2=g,b^a=be,e^a=eg,c^b=cg,h^b=h^521084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27290163, #27290165, #27290166, … |
| maximal normal subgroup of | #27290163, #27290165, #27290166, … |
| maximal quotient of | #27353075, #27353114, #27353126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13099);