Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C7×#1781 ⋊ C2 |
| Sylow | C7 ⋊ #8534 |
1408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^8,7|a^2=f,b^a=bd,c^a=ce,d^a=dg,i^a=i^6,e^b=eh,f^b=fg,i^b=i^6,d^c=dh136 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#8534, #72260036 |
| maximal normal subgroup of | D7×#8534, #72260036 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 62140);