Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#1357 ⋊ C2 |
| Sylow | C7 ⋊ #12310 |
406 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 59 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|d^2=f,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,g^a=gh,i^a=i^6,d^b=df,e^b=eg,g^b=gh,d^c=dg,e^c=eg,f^c=fh,g^c=gh,i^c=i^6103 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#12310, #72259974, #72260009 |
| maximal normal subgroup of | D7×#12310, #72259974, #72260009 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 82962);