Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C71×#1746 ⋊ C2 |
| Sylow | C71 ⋊ #22276 |
1050 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 227 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=g,b^2=eg,c^2=efh,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^70,c^b=ce,d^b=dh2012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 183412);