Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C71×#1313 ⋊ C2 |
| Sylow | C71 ⋊ #11404 |
298 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 147 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=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bf,c^a=ch,e^a=eh,d^b=dh,i^c=i^701628 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 78567);