Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C71 ⋊ #8355 |
774 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 167 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=f,b^2=h,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^70,d^b=dh,e^b=eg,f^b=fgh,d^c=dg1586 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 61126);