Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M64×C71 ⋊ C2 |
| Sylow | C71 ⋊ #33981 |
466 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=be,c^a=ch,e^a=ef,f^a=fg,g^a=gh,i^a=i^70,e^b=ef,f^b=fg,g^b=gh,i^b=i^702852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 327714);