Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C71×#1290 ⋊ C2 |
| Sylow | C71 ⋊ #7986 |
546 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 157 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=e,b^2=f,c^2=g,d^2=gh,e^2=g,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,e^b=eh,i^c=i^701184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 59461);