Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C71×#1288 ⋊ C2 |
| Sylow | C71 ⋊ #10380 |
390 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=d,b^2=dg,e^2=gh,f^2=g,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,c^b=cf,e^b=eh,i^b=i^70,d^c=dg,e^c=egh,f^c=fg,i^c=i^701154 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 72757);