Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C71 ⋊ #7595 |
630 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 155 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=e,b^2=g,d^2=g,e^2=h,b^a=bd,c^a=cg,d^a=df,i^a=i^70,d^b=dg,e^b=efg2012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 57657);