Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C71 ⋊ #18138 |
1054 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 183 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=h,b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,i^a=i^70,e^b=eg,f^b=fh,e^c=eh1577 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 141984);