Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C71 ⋊ #7432 |
210 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^8,71|a^2=d,b^2=eg,c^2=fgh,e^2=h,f^2=h,b^a=bc,c^a=ce,e^a=eg,i^a=i^70,c^b=cf,d^b=defgh,e^b=eh,g^b=gh,d^c=dgh,e^c=eh941 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 57165);