Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C71 ⋊ #12624 |
456 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^8,71|a^2=e,b^2=f,c^2=e,e^2=h,b^a=bd,c^a=ch,f^a=fg,d^b=dg,g^b=gh,i^b=i^70,f^d=fh1586 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 84725);