Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #353×C73 ⋊ C4 |
| Sylow | C73 ⋊ #7504 |
336 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|a^2=d,b^2=e,c^2=gh,e^2=h,f^2=h,b^a=bc,c^a=cf,e^a=eg,f^a=fg,g^a=gh,c^b=ch,d^b=dfg,i^b=i^27,d^c=dgh,e^d=eh,f^d=fh,i^e=i^72262 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1084768);