Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #11992 |
412 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 87 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=e,d^2=g,e^2=fg,f^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,g^a=gh,i^a=i^6,d^b=dg,e^b=efgh,f^b=fh,e^c=eh124 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#11992, #72259925, #72259998 |
| maximal normal subgroup of | D7×#11992, #72259925, #72259998 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 81100);