Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q64×C73 ⋊ C2 |
| Sylow | C73 ⋊ #13666 |
288 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=h,c^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,d^b=df,f^b=fg,g^b=gh,i^b=i^72,i^c=i^721417 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 90234);