Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ C4×#108 |
228 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=e,b^2=f,c^2=de,d^2=g,e^2=g,f^2=g,b^a=bd,d^b=dg,e^b=eg,h^c=h^52784 conjugacy classes — view the full character table.
| maximal subgroup of | #27294519, #27294523, #27294527, … |
| maximal normal subgroup of | #27294519, #27294523, #27294527, … |
| maximal quotient of | #27275272, #27275276, #27275280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4411);