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 ⋊ #1778 |
220 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 113 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,c^a=cg,h^a=h^52,d^b=dg,e^b=eg1084 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1778, C2×#20274622, #27382198, … |
| maximal normal subgroup of | D53×#1778, C2×#20274622, #27382198, … |
| maximal quotient of | #27275290, #27275295, #27275300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4417);