Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C71 ⋊ #7375 |
228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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=d,b^2=e,d^2=f,e^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^70,c^b=cg,d^b=deh,g^b=gh,i^b=i^70,d^c=dgh,e^c=eh,e^d=eh1364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 56995);